Нелинейные экситон-поляритонные свойства планарных оптических резонаторов на основе галогенидных перовскитов тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Машарин Михаил Алексеевич

• Машарин Михаил Алексеевич
• кандидат наук
• 2023

Оглавление диссертации кандидат наук Машарин Михаил Алексеевич

Реферат

Synopsis

Introduction

Chapter 1. Literature review

1.1 Strong light-matter coupling regime in photonic cavities with embedded excitonic materials

1.1.1 Theoretical description

1.1.2 Exciton-polariton-driven nonlinear effects

1.1.3 Exciton-polariton condensation

1.2 Halide perovskites as a prospective family of materials for photonic strutures

1.2.1 Crystal structure and basic features

1.2.2 Optical properties

1.3 Planar photonic cavities for exciton-polariton systems

1.3.1 Planar waveguides, photonic crystal slabs, and metasurfaces

1.3.2 Bound states in the continuum and exceptional points

1.4 Conclusion on Chapter

Chapter 2. Experimental methods

2.1 Perovskite photonic crystal slab fabrication

2.1.1 Thin film nanoimprinting

2.2 Fabrication of the perovskite single-crystal self-resonating structures

2.2.1 Perovskite nanowire synthesis

2.2.2 Perovskite nanocube synthesis

2.3 Scanning electron microscopy

2.4 Atomic force microscopy

2.5 Optical microscopy and angle-resolved spectroscopy

2.5.1 Angle-resolved imaging and spectroscopy with temperature

dependence

2.5.2 The study of guided modes dispersion below air light cone

2.6 Conclusion on Chapter

Chapter 3. Polaron-enhanced nonlinear exciton-polariton

blueshift in photonic crystal slabs based on halide

perovskites

3.1 Exciton-polariton nonlienarities in MAPbI3 photonic crystal slab

3.2 Room-temperature exciton-polariton nonlinearities in MAPbBr3 photnic crystal slab

3.3 Theoretical model of polaron-mediated exciton-polaritons nonlinearities

3.4 Conclusion of Chapter

Chapter 4. Spectral redshift of the polariton-assisted amplified spontaneous spectra in the perovskite planar photon

cavities

4.1 Theoretical description of the exciton-polariton Bose dynamics

4.2 Experimental observation of polariton stimulated relaxation at cryogenic temperatures

4.3 Control of the stimulated polariton relaxation at room temperature

in perovskite planar photonic cavities

4.4 Conclusion on chapter

Chapter 5. Room-temperature exceptional-point-driven polariton

condensation in the MAPbBr3 photonic crystal slab

5.1 Photonic dispersion surface of the fabricated MAPbBr3 PCS

5.2 Polariton amplified stimulated emission and polariton condensation

5.3 Theoretical model of exceptional points appearance

5.4 Conclusion of Chapter

Conclusion

List of figures

List of tables

References

Acknowledgements

Appendix A. Fitting of the polariton linewidths in perovsite PCSs

Appendix B. Rabi quenching saturation rates expressions

Appendix C. Texts of author's key publications

Реферат

Краткое содержание диссертации

Введение диссертации (часть автореферата) на тему «Нелинейные экситон-поляритонные свойства планарных оптических резонаторов на основе галогенидных перовскитов»

Актуальность темы

На сегодняшний день вычислительные электронные устройства приближаются к своим фундаментальным пределам производительности, размеров и эффективности. Для преодоления этих ограничений и осуществления нового скачка в развитии вычислительных технологий нужен переход к принципиально новым системам и устройствам. Такой новый подход может предложить оптические системы, которые используют фотоны в качестве основных носителей информации [1]. Фундаментальный переход к фотонным устройствам, таким как транзисторы, переключатели, логические элементы и другие, использующиеся в современных электронных приборах, требует разработки систем с одновременно сильным и сверхбыстрым нелинейным оптическим откликом. Одним из перспективных подходов для этого являются экситон-поляритоны - гибридные квазичастицы, объединяющие в себе свойства света и вещества, которые формируются в оптических резонаторах с сильной локализацией поля в экситонном материале. Более того, эти квазичастицы могут вызывать эффект неравновесной экситон-поляритонной конденсации Бозе-Эйнштейна, достигаемый как под действием оптической [2], так и под действием электрической накачки [3]. На данный момент существуют две значительные проблемы, которые необходимо преодолеть, прежде чем экситон-поляритоны смогут широко использоваться в реальных фотонных устройствах [4]. Во-первых, это проблема недостатка экситонных материалов, которые одновременно могут поддерживать стабильные экситонные состояния при комнатной температуре, являются дешевыми в производстве с возможностью эффективного масштабирования, а также обладают сильной оптической нелинейностью. Материалы, использующиеся в экситон-поляритонных системах сегодня, такие как полупроводниковые квантовые ямы (на основе таких материалов как СаЛэ, С^е, ZnO), монослои дихалькогенидов переходных металлов или полимерные полупроводники обладают некоторыми из этих качеств, однако каждый имеет свои ограничения [5-9]. Во-вторых, широко используемые вертикальные

брэгговские резонаторы в экситон-поляритонных системах ограничены из-за своей высокой стоимости производства и громоздкой вертикальной геометрией, что делает их плохо совместимыми с планарными фотонными системами на чипе, чего не скажешь о планарных фотонных резонаторах, такие как, например, фотонно-кристаллические волноводы [10], которые могут быть изготовлены дешевыми методами, такими как прямая лазерная абляция [11] или наноимпринт литография [12].

Галогенидные перовскиты являются перспективными материалами для решения обеих проблем, так как с одной стороны обладают высокой энергией связи экситона, могут быть синтезированы недорогими методами растворной химии и демонстрируют сильные нелинейные оптические свойства [1315], ас другой - имеют высокий показатель преломления, что позволяет создавать на их базе различные фотонные резонаторы с сильной локализацией оптического поля внутри активной среды. В частности, объемные перовскиты, такие как МАРЫз, МЛРЬБгз и СэРЬБг3 являются более стабильными с точки зрения лучевой стойкости и не подвержены эффектам квантового ограничения в сравнении с перовскитными квантовыми точками или слоистыми квазидвумерными перовскитами [16]. Более того, по этим материалам уже опубликованы тысячи работ в области фотоники и оптоэлектроники, что позволяет уверенно воспроизводить технологии их синтеза для дальнейших исследований и использования в экситон-поляритонных системах [17].

Режим сильной экситон-фотонной связи в объемных галогенидных перовскитах уже был исследован в системах на основе вертикальных брэгговских резонаторов, в том числе был продемонстрирован эффект неравновесной экситон-поляритонной конденсации Бозе-Эйнштейна при комнатной температуре [14]. Более того, в литературе уже были показаны различные первоскитные фотонные резонаторы, поддерживающие высокодобротные оптические состояния, такие как фотонно-кристаллические волноводы (ФКВ) [18], метаповерхности [19], резонаторы Фабри-Перо [20] и другие. Однако, несмотря на то, что в таких структурах должны выполняться все необходимые условия для формирования сильной экситон-фотонной связи, как со стороны экситонного материала, так и со стороны оптического резонатора, экситон-поляритонные состояния и их свойства в подобных системах до сих пор не были подробно изучены.

С учетом вышеизложенного, экстион-поляритонные системы на основе перовскитных планарных фотонных резонаторов могут обеспечить прорыв в области поляритоники, что приблизит использование таких структур в реальных оптоэлектронных устройствах и оптических вычислительных элементах на чипе.

Целью диссертации является экспериментальное и теоретическое исследование режима сильной экситон-фотонной связи в планарных оптических резонаторах на основе объемных галогенидных перовскитов, а также изучение их оптических нелинейных эффектов, роли экситон-поляритонов в вынужденном излучении и явления неравновесной экситон-поляритонной конденсации Бозе-Эйнштейна.

Для достижения цели были сформулированы следующие задачи диссиртационного исследования:

1. Экспериментальное исследование режима сильной экситон-фотонной связи и нелинейного поляритонного синего смещения моды при резонансной импульсной накачке в фотонно-кристаллических волноводах на основе поликристаллических плёнок перовскитов МЛРЫз и МЛРЬБг3.

2. Экспериментальное исследование роли экситон-поляритонов в вынужденном излучении, возникающее в нелинейном режиме при нерезонансной фемтосекундной оптической накачке, в планарных структурах на основе бромидных перовскитов МЛРЬБг3 и СэРЬБг3.

3. Экспериментальное исследование явления неравновесной экситон-поляритон конденсации Бозе-Эйнштейна в перовскитном фотонно-кристаллическом волноводе при комнатной температуре.

Основные положения, выносимые на защиту

1. В планарных резонаторах на основе органо-неорганических галогенидных перовскитов в режиме сильной экситон-фотонной связи при резонансной фемтосекундной накачке наблюдается увеличенный поляронными эффектами нелинейный синий спектральный сдвиг экситон-поляритонных дисперсий, превышающий 19 мэВ для состава перовскита МЛРЬ13 при температуре 6 К и превышающий 6 мэВ для МЛРЬБг3 при комнатной температуре.

2. В экстион-поляритонных структурах на основе свинцово-бромидных перовскитов при комнатной температуре, с увеличением плотности

энергии в фемтосекундном импульсе накачки наблюдается красный сдвиг спектрального положения максимума усиленного спонтанного излучения на значения, достигающие 16 мэВ, обусловленный стимулированной релаксацией поляритонов по энергии.

3. В одномерном фотоно-кристаллическом волноводе на основе перовскита МАРЬБгз на стеклянной подложке при пересечении дисперсий экситон-поляритонных мод, распространяющихся навстречу друг к другу, на частоте, лежащей в спектральной области усиленного спонтанного излучения, пороговым образом, начиная с плотности энергии импульса фемтосекундной накачки, около 30 мкДж/см2, возникают исключительные точки. Благодаря усиленной плотности оптических состояний в исключительных точках, на соответствующих им волновых векторах и частоте при комнатной температуре наблюдается поляритонная конденсация, проявляющаяся в узкополосном (менее 1 мэВ) вынужденном излучении с высокой направленностью (расхождение менее 1 градуса).

Научная новизна

1. В перовскитовом фотонно-кристаллическом волноводе, поддерживающий режим сильной экситон-фотонной связи, экспериментально достигнуто рекордное значение экситон-поляритонного нелинейного синего спектрального смещения до 19.7 мэВ, что на 51% выше достигнутым ранее значениям в системе на основе WS2. Впервые продемонстрировано влияние поляронных эффектов на экситон-поляритонные состояния и их оптические нелинейности.

2. Впервые доказана непосредственная роль экситон-поляритонов в вынужденном излучении планарных структур на основе бромидных перовскитов, проявляющаяся в стимулированной релаксации поляритонов в более низкие по энергии состояния и, как следствие, изменение формы спектров вынужденного излучения при увеличении плотности энергии импульса оптической нерезонансной накачки.

3. Впервые продемонстрировано явление неравновесной экситон-поляри-тонной конденсации Бозе-Эйнштейна в планарном перовскитном фотонно-крис-таллическом волноводе при комнатной температуре, возникающее вследствие формирования исключительных точек в нелинейном режиме под действием нерезонансной оптической накачки.

Теоретическая и практическая значимость работы заключается в комплексном изучении нелинейных оптических эффектов, возникающих в перовскитных планарных фотонных резонаторах, поддерживающих режим сильной экситон-фотонной связи. На основе экспериментальных наблюдений предложено феноменологическое описание поляронных эффектов, значительно влияющие на экситон-поляритонные состояния и их нелинейные свойства. Также в диссертации проводится исследование природы вынужденного излучения в перовскитных фотонных структурах, которое может поспособствовать дальнейшему эффективному развитию сферы перовскитной нанофотоники и в перспективе посодействовать созданию недорогих оптоэлектронных устройств. Был продемонстрирован принципиально новый подход генерации лазерного излучения в перовскитных структурах, заключающийся в поляритонной конденсации на основе исключительных точек, что открывает новые пути к созданию недорогих поляритонных лазеров без инверсии населенностей в планарных наноразмерных структурах, которые в дальнейшем могут найти широкое применение в области оптоэлектроники.

Достоверность результатов диссертации обеспечивается применением современных методов исследования, гарантирующих хорошую воспроизводимость полученных данных. Экспериментальные данные количественно описываются теоретическими моделями и результатами численного моделирования, а также не противоречат ранее опубликованным научным работам. Результаты были апробированы как на всероссийских, так и на международных конференциях, а также опубликованы в авторитетных рецензируемых международных журналах.

Аппробация работы

1. V International Conference on Metamaterials and Nanophotonics, METANANO 2020, онлайн, 14 - 18 сентября 2020;

2. II Московская осенняя международная конференция по перовскитной фотовольтаике, Москва, 26 - 28 октября 2020;

3. School on Advanced Light-Emitting and Optical Materials SLALOM 2021, Владивосток, 28 - 30 июля 2021;

4. VI International Conference on Metamaterials and Nanophotonics, METANANO 2021, онлайн, 13 - 17 сентября 2021;

5. Международная школа-конференция по оптоэлектронике, фотонике и нанобиоструктурам Spb OPEN 2022, Санкт-Петербург, 24-27 мая 2022;

6. International Conference Nanophotonics and micro/nano optics NANOP, Париж, 25-27 октября 2022;

7. Низкоразмерный семинар ФТИ им. Иоффе, Санкт-Петербург, 7 февраля 2022;

8. UNAM Scientific Seminar, Университет Билкент, UNAM, Анкара, 22 июня 2022;

Публикации

Основные результаты по теме диссертации изложены в 5 публикациях, индексируемые в базах данных Scopus и Web of Science.

Личный вклад автора заключается в отработке методов изготовления перовскитных фотонно-кристаллических волноводов, характеризации морфологии образцов методом атомно-силовой микроскопии, создании экспериментальной установки для спектроскопии с угловым разрешением и проведении с её помощью оптических экспериментов при криогенных и комнатной температурах, численном моделировании спектров отражения с угловым разрешением перовскитных периодичных структур, численном моделировании взаимодействия утекающих мод перовскитного ФКВ, обработке и анализе экспериментальных данных. Автор принимал участие в оптических экспериментах по измерению поляритонных волноводных дисперсий с использованием линзы твердой иммерсии, а также в формулировке целей и постановке задач диссертации, непосредственно участвовал в написании текстов и подготовке рисунков для научных статей.

Объём и структура работы

Диссертация состоит из введения, 5 глав, заключения и 3 приложений. Полный объём диссертации составляет 224 страницы, включая 67 рисунков и 4 таблицы. Список литературы содержит 194 наименования.

Основное содержание работы

Во введении диссертации излагаются цели, задачи, а также формулируются положения, выносимые на защиту. Обосновывается актуальность, достоверность и значимость работы, описывается личный вклад автора.

В Главе 1 представлен обзор литературы, посвященный режиму сильной экситон-фотонной связи в различных системах.

В первом разделе обсуждается понятие экситон-поляритонов, а также обусловленные этими квазичастицами нелинейные оптические свойства различных систем, включая явление экситон-поляритонной конденсации Бозе-Эйнштейна (поляритонной конденсации). В разделе также представлен обзор предыдущих работ по данной тематике и формулируются основные проблемы, мотивирующие поиск новых экситонных материалов и дизайнов оптических резонаторов.

Во втором разделе представлен обзор литературы, посвященной галогенидным перовскитам с акцентом на их экситонные и оптические свойства. В этой части демонстрируется высокий потенциал этих материалов для использования их в экситон-поляритонных системах в качестве активных сред.

В последнем разделе представлен обзор существующих планарных систем с высокой оптической добротностью и обсуждается потенциал их применения в экситон-поляритонных системах вместо широко используемых в данной области вертикальных брэгговских резонаторов.

В Главе 2 описаны экспериментальные методы синтеза образцов, методы характеризации их морфологий, а также использованные в работе методы оптической спектроскопии. В частности показаны методы синтеза перовскитных ФКВ на основе поликристаллических тонких плёнок MAPbBr3 и MAPbI3, включающие в себя центрифугирование перовскитного раствора (spin coating) с последующей наноимпринт литографией. Приведено описание методов изготовления монокристаллических перовскитных структур, таких как нанопроволоки и нанокубоиды CsPbBr3. Описаны методы характеризации морфологии, такие как сканирующая электронная микроскопия (СЭМ) и атомно-силовая микроскопия (АСМ). В главе приведено подробное описание методов спектроскопии с угловым разрешением, включая эксперименты при криогенных температурах и подходы к измерению дисперсий волноводных мод ниже линии света.

Глава 3 диссертации посвящена исследованию влияния поляронных эффектов на экситон-поляритонные состояния, в планарных ФКВ на основе галогенидных перовскитов метиламмония иодида свинца (MAPbI3) и метиламмония бромида свинца (MAPbBr3), а также на нелинейные оптические свойства этих структур, проявляющиеся под воздействием резонансной

импульсной оптической накачки. Предложено феменологическое объяснение наблюдаемых рекордно высоких значений нелинейного поляритонного синего смещения, заключающиеся в сильном влиянии поляронных эффектов, которые представляют собой связывание экситонных состояний с продольными фононными модами в материале. Эта концепция легла в основу теоретической количественной модели.

Первая часть главы посвящена экспериментальному исследованию режима сильной экситон-фотонной связи, возникающего в ФКВ на основе тонкой плёнки перовскита МАРЬ13, и его нелинейному оптическому отклику при криогенных температурах. Поскольку энергия связи экситона в МАРЬ13 при комнатной температуре значительно меньше тепловой энергии (Е^т = 12 мэВ, Е^т = 25 мэВ), экситон-поляритоны при нормальных условиях не наблюдаются [21].

При температуре около 150 К МАРЬ13 демонстрирует фазовый переход, переходя из высокотемпературной тетрагональной 14/шсш в орторомбическую Рпша фазу, что резко изменяет его ширину запрещенной зоны и положение экситонного резонанса [22]. В связи с этим исследования проводились до и после перехода при температурах 170 К и 6 К. Чтобы подтвердить реализацию режима сильной экситон-фотонной связи, были измерены спектры фотолюминесценции (ФЛ) с угловым разрешением при 170 К и 6 К, показанные на Рисунках 1а и 1Ь, соответственно. Наблюдаемые утекающие моды ФКВ демонстрируют ярко выраженное искривление вблизи экситонного резонанса, типичное для экситон-поляритонных состояний [23]. Из полученных данных были определены дисперсии утекающих мод, которые аппроксимировались при помощи модели двух связанных осцилляторов [23]. Результат аппроксимации, хорошо согласующийся с экспериментальными наблюдениями (Рисунки 1а и 1Ь), позволяет определить значения коэффициента экситон-фотонной связи до и расщепления Раби ^д, как д0 = 17.9 мэВ, ^д = 35.2 мэВ при 170 К и д0 = 19.6 мэВ, ^д = 35.7 мэВ при 6 К. Полученные значения удовлетворяют критериям режима сильной экситон-фотонной связи [23], что подтверждает существование экситон-поляритонных состояний в исследуемой структуре при указанных температурах. На основе полученных значений коэффициента экситон-фотонной связи были также рассчитаны коэффициенты Хопфилда, квадрат модуля которых определяет фракции экситона |2 и фотона |2

Рисунок 1 — (а,Ь) Спектры ФЛ с угловым разрешением перовскитного ФКВ МЛРЬ13 при 170 К и 6 К. Желтые и красные линии соответствуют дисперсии несвязанного фотона и экситона. Зеленые пустые точки соответствуют экспериментально определенной поляритонной моде. Синие сплошные линии соответствуют результату оптимизации модели двух связанных осцилляторов. (с, ^ Расчетные экситонные (красные) и фотонные (желтые) коэффициенты

Хопфилда [24]

в поляритонном состоянии в зависимости от компоненты волнового вектора кх в направлении периодичности образца [23], показанные на Рисунках 1с и Ы.

Нелинейные поляритонные эффекты проявляются при увеличении числа экситон-поляритонов в системе, что приводит к росту величины их кулоновского взаимодействия друг с другом, а также уменьшению расщепления Раби. Оба этих механизма вызывают нелинейное синее смещение нижней поляритонной ветви [25; 26]. Для изучения этого явления в ФКВ на основе МЛРЬ13 были проведены измерения спектрального положения поляритонной моды при резонансной фемтосекундной накачке с увеличением плотности энергии импульса для обеих температур. Спектральное положение максимума

резонансной накачки (однозначно связанного с компонентой волнового вектора в плоскости кх) было выбрано таким образом, чтобы лежать на дисперсионной ветви поляритонной моды для различных величин экситонных коэффициентов Хопфилда (Рисунки 2а и 2Ь). Спектральное положение поляритонной моды для различных величин энергии импульса оценивалось путем аппроксимации измеренных в пределах частотной полосы лазерного импульса спектров отражения, содержащих поляритонный резонанс. Спектры отражения аппроксимировались при помощи функции Фано, вычисляя спектральное положение и ширину линии поляритонной моды [27] (Рисунки 2с и 2^. Зависимости величины синего смещения полирятонной ветки от плотности энергии импульса накачки для всех коэффициентов Хопфилда, измеренных при 170 К и 6 К, показаны на Рисунках 2е и 2£. Наибольшие значения поляритонных синих смещений составляющие ДЕ=13 мэВ при 170 К и ДЕ=19.7 мэВ при 6 К, наблюдались при меньших значениях компоненты волнового вектора кх, соответствующие более высоким экситонным коэффициентам Хопфилда \Хь\2. Насколько известно автору значение поляритонного синего смещения в 19.7 мэВ является рекордным для экситон-поляритонных систем, достигнутым экспериментально на сегодняшний день.

Во второй части главы рассматривается ФКВ на основе МАРЬВг3. В этом материале экситоны остаются стабильными при комнатной температуре благодаря более высокой энергии связи. При этом в МАРЬВг3, как и в МАРЬ13, наблюдаются ярко выраженные поляронные эффекты [21]. Исследуемый ФКВ на основе МАРЬВг3 имеет ту же геометрию одномерной решетки с периодом 750 нм, что и предыдущий образец.

Следуя той же методологии, что и в предыдущем эксперименте, были измерены спектры ФЛ с угловым разрешением, при различных температурах. Измеренные спектры демонстрируют излучение несвязного экситона без выделенной направленности и излучение утекающих экситон-поляритонных мод, обладающих ярко выраженной дисперсией (Рисунок 3а). Для каждой температуры были определены положения экситонного резонанса Ех и значения коэффициента экситон-фотонной связи д0 путём аппроксимации извлеченной поляритонной ветви при помощи модели двух связанных осцилляторов [23; 28]. Результаты аппроксимации приведены на Рисунке 3а, из которых видно, что модель позволяет хорошо описать экспериментальные данные.

Рисунок 2 — (a, b) Спектры отражения s-поляризованного света с угловым разрешением от ФКВ, изготовленного на основе МАРЫз при 170 K и 6 K. Цветные эллипсы соответствуют спектрам и компонентам волнового вектора кх использующихся в качестве резонансных оптических накачек. (c, d) Эволюция спектров поляритонной моды, измеренных в пределах спектральной полосы лазера накачки, с увеличением плотности энергии импульса. (e,f) Зависимости значения поляритонного синего смещения от плотности энергии импульса накачки для разных коэффициентах Хопфилда. Пунктирными линиями показаны результаты теоретического численного моделирования [24]

/ /

7/

110К

200К

0.4 0.6

К'К

Temperature, К

Temperature, К

Рисунок 3 — (а) Измеренные с угловым разрешением спектры ФЛ ФКВ на основе МАРЬВг3 с изображенными дисперсией несвязного фотона (оранжевые прямые), уровнями несвязанного экситона (красные прямые) и дисперсиями утекающих мод экситон-поляритона (зеленые кривые) при различных температурах. (с, ^ Рассчитанные зависимости положения экситонного резонанса и коэффициента экситон-фотонной связи д0 от температуры [29]

Спектральное положение экситонного резонанса демонстрирует сильную температурную зависимость, которая согласуется с предыдущими исследованиями (Рисунок 3Ь) [21; 30]. Наблюдаемое красное смещение с понижением температуры, объясняется линейными поляронными эффектами, а именно изменением поляронной добавки в экситонном потенциале с изменением энергии фононов [21]. На Рисунке 3с показаны расчетные значения коэффициента связи д0, которые удовлетворяют критериям режима сильной экситон-фотонной связи для всех температур вплоть до 300 К. Увеличение коэффициента связи с понижением температуры объясняется ростом силы осциллятора экситона в материале [31].

Аналогичным образом были исследованы нелинейные оптические поляритонные эффекты в ФКВ, на основе МАРЬВг3. В отличие от экспериментов с МАРЬ13, эти измерения проводились при комнатной

Р1иепсе, мЛ/ст2 Р1иепсе, ^/ст2

Рисунок 4 — (а) Экспериментально измеренное значение нелинейного синего поляритонного смещения в зависимости от плотности энергии импульса резонансной накачки для различных экситонных коэффициентов Хопфилда. Пунктирные линии соответствуют результатам теоретической модели. (Ь) Результат численного моделирования значения нелинейного поляритонного синего смещения при более высоких плотностях энергии имульса

накачки [29]

температуре. Были выбраны три значения экситонного коэффициента Хопфилда, соответствующие различным спектральным положениям и компонентам волнового вектора кх резонансной накачки. Результаты измерений значений нелинейного синего поляритонного смещения как функции плотности энергии импульса накачки приведены на Рисунке 4а. Наибольшее измеренное значение синего поляритонного смещения для самой высокой доли экситонов составило 6.4 мэВ. Отметим однако что, максимальное наблюдаемое значение синего поляритонного смещения было экспериментально ограничено шириной спектральной полосы лазера накачки. Теоретическая модель нелинейного оптического поляритонного отклика в данных системах, разработанная В. Шахназаряном, позволила не только описать полученные результаты, показанные пунктирными линиями на Рисунке 4а, но и оценить максимально достижимые значения нелинейного синего поляритонного смещения в ФКВ на основе МЛРЬБгз (Рисунок 4Ь).

Последняя часть главы посвящена разработанной теоретической модели, описывающая феномен нелинейного синего поляритонного смещения с учетом

поляронных эффектов в МАРЬ13 при 170 К и 6 К и в МАРЬВг3 при комнатной температуре. Как показано на Рисунках 2е-£ и 4а, результаты численного моделирования хорошо согласуются с экспериментальными данными при разных значениях коэффициента Хопфилда для обоих перовскитов. Теоретическое описание показало, что поляронные эффекты приводят к изменению водородоподобного ридбергского потенциала экситона, приводя к изменениям в соотношениях между боровским радиусом экситона, определяющий максимально достижимую плотность экситонов (соответствующую переходу Мотта), и константами нелинейного взаимодействия. Это, в свою очередь, приводит к усилению нелинейного оптического поляритонного отклика, позволяя получать рекордно высокие значения нелинейного синего поляритонного смещения.

Таким образом, в главе впервые показано, что в галогенидных перовскитных ФКВ на основе МАРЬ13 и МАРЬВг3 режим сильной экситон-фотонной связи может быть реализован при высоких температурах, вплоть до 300 К. Этот результат достижим благодаря высокой энергии связи экситона, обеспечиваемой линейными поляронными эффектами. Также было обнаружено, что поляроны усиливают и нелинейные оптические свойства поляритонов, увеличивая нелинейное полряитонное синее смещение за счет модификации экситонного потенциала. Это, в свою очередь, позволяет экспериментально получить рекордно высокое значение синего смещения, равное 19.7 мэВ в МАРЬ13 ФКВ при 6 К.

Список литературы диссертационного исследования кандидат наук Машарин Михаил Алексеевич, 2023 год

+ ^ —

Vke =

vhh =

e

2

4tc£o

2

4n +

£sq2

e

4n£o

4n + 4^£m

t + y 1

£sq

2

£

1 + Q

2

^k =

na

B

(B.9)

(B.10)

(B.11)

(B.12)

[1 + (aB k)2]2

are the Fourier-transformed expression of the potentials and the exciton wavefunc-tion, respectively. Thus, the saturation rates are: [26]

El^k |2^k

s = 2-

E^

S2 = 2

q

E l^k |2^k E l^k' |4 - E l^k» |4^k» k k' k"

E^

(B.13)

(B.14)

2

e

3

Appendix C Texts of author's key publications

NANOw

T E R

J)

pubs.acs.org/NanoLett

Polaron-Enhanced Polariton Nonlinearity in Lead Halide Perovskites

Mikhail A. Masharin, Vanik A. Shahnazaryan, Fedor A. Benimetskiy, Dmitry N. Krizhanovskii, Ivan A. Shelykh, Ivan V. Iorsh, Sergey V. Makarov, and Anton K. Samusev*

Cite This: Nano Lett. 2022, 22, 9092-

Read Online

ACCESS

lilil Metrics & More

lUi Article Recommendations

.si) Supporting Information

O 3

H 3

& ü

Polaron-mediated exciton-polaritons in lead halide perovskite

Polariton-enhanced polariton blueshift

Polaron potential

Coulomb potential

ABSTRACT: Exciton-polaritons offer a versatile platform for realization of all-optical integrated logic gates due to the strong effective optical nonlinearity resulting from the exciton—exciton interactions. In most of the current excitonic materials there exists a direct connection between the exciton robustness to thermal fluctuations and the strength of the exciton—exciton interaction, making materials with the highest levels of exciton nonlinearity applicable at cryogenic temperatures only. Here, we show that strong polaronic effects, characteristic for perovskite materials, allow overcoming this limitation. Namely, we demonstrate a record-high value of the nonlinear optical response in the nanostructured organic—inorganic halide perovskite MAPM3, experimentally detected as a 19.7 meV blueshift of the polariton branch under femtosecond laser irradiation. This is substantially higher than characteristic values for the samples based on conventional semiconductors and monolayers of transition-metal dichalcogenides. The observed strong polaron-enhanced nonlinearity exists for both tetragonal and orthorhombic phases of MAPbI3 and remains stable at elevated temperatures. KEYWORDS: exciton-polaritons, polariton nonlinearity, polarons, planar cavity, nanoimprint, perovskites

• •vi«•• • •

• • •••f

hi® ft: • • • , ,

; » f-f- ff-* 4-f 1 i

ixixinii-n

N

TS -O

£ * £

Q 5

Excitons are solid state analogues of a hydrogen atom, appearing due to the Coulomb attraction between an electron in a conduction band and a hole in a valence band. In direct band-gap semiconductors they can be created optically by resonant absorption of photons. If the energy of an exciton—photon interaction exceeds all characteristic broad-enings in a system, the regime of strong light—matter coupling is achieved. It is characterized by the emergence of hybrid halflight half-matter elementary excitations, known as exciton-polaritons. To drive a system into this regime, one needs to reach an efficient confinement of the electromagnetic field, which can be achieved in semiconductor microcavities,1 optical waveguides,2 photonic bound states in a continuum,3 or leaky modes of photonic crystal slabs.4 Exciton-polaritons demonstrate a set of remarkable properties, which makes them ideal candidates for both the fundamental study of a variety of quantum collective phenomena5 and modern optoelectronic applications.6 In particular, from their photonic component they inherit an extremely small effective mass and long decoherence time, while the presence of the excitonic component allows for efficient polariton—polariton interactions, leading to the onset of a robust nonlinear optical response. The latter is experimentally revealed as a blueshift of a polariton line with the increase in pumping power.

From a technological perspective, it is clearly highly desirable to have a material platform that combines the thermal stability of excitons and polaritons with a strong

degree of their optical nonlinearity. For more than a decade, the study of the nonlinear excitonic response was focused on conventional semiconductor platforms, including both narrowband-gap (e.g., CdTe and GaAs — ) and wide-band-gap materials (e.g., GaN12 14 and ZnO15,16), where excitons are well described by the hydrogen model.

Essentially, while the blueshift per single polariton tells us about how well the nonlinear polariton systems perform at low excitation density, the maximum value of the blueshift enabled by a polariton system characterizes its nonlinear optical response at high density. For wide-band-gap materials excitons have a much smaller effective size aB (exciton Bohr radius), which decreases the exciton—exciton interaction constant Vxx (often referred to as g and defined mostly by the processes of electron and hole exchange17), and thus the blueshift per polariton is reduced also. At the same time the reduction of the Bohr radius substantially increases the Mott transition density. This, in general, allows reaching greater values ofthe maximum possible blueshift of an excitonic line.

Received: September 6, 2022 Revised: October 30, 2022 Published: November 7, 2022

ACS Publications

© 2022 American Chemical Society

Letter

9092

Nano Letters

pubs.acs.org/NanoLett

Figure 1. (a) Estimated values of the maximum blueshift induced by exciton-exciton interactions in the quadratic approximation, AEmax = Vxx^max/2 — IVxx2lnmax, where «max = 0.05/aB and d = 2, 3 are the densities corresponding to the maximum blueshift for 2D and 3D materials, respectively. The values corresponding to the hydrogen model, applicable to the vast majority of conventional semiconductors (GaAs, CdTe, GaN, ZnSe, and CuBr are taken as examples), lie on straight blue (3D) and orange (2D) lines. The points below these lines correspond to materials that are suboptimal for optical nonlinearity (e.g., TMD monolayers, red circle) and the points above these lines, such as the MAPM3 perovskite considered in the present work (dark blue circles), to optimal materials. The values of nmax for the exciton-polarons in perovskites and excitons in TMD monolayers are distinct from those of 3D and 2D hydrogen models and depend on particular material parameters. (b) Sketch of a polaron-mediated exciton state, visualizing the polaron enhancement of exciton binding energy. The polaronic renormalization of Coulomb interactions breaks the Rydberg type scaling between exciton binding energy and Bohr radius, resulting in the modification of exciton optical nonlinearity. (c) Sketch of the experimental geometry used in this work. A photonic crystal slab is fabricated by a nanoimprint lithography method. The corresponding leaky photonic mode couples with an excitonic transition in bulk MAPM3 perovskite, giving rise to polariton modes, which are analyzed in nonlinear reflectance measurements performed under a resonant (in angle and frequency) laser pump. The incident wavevector and its in-plane component are denoted by ko and kx, respectively. (d) Calculated lower polariton dispersion (green line) resulting from the strong coupling between the exciton (light red dashed line) and the leaky photonic crystal modes (yellow dashed line). The increase of the resonant pump leads to a blueshift of the lower polariton mode (solid blue line) caused by many-body renormalization of spectrum due to the exciton—exciton interactions and quenching of the Rabi splitting (see the main text for the corresponding discussion).

Letter

The blueshift value can be evaluated as

AEnax « V^tlmJl- IV^In^ (l)

Here «max = VXx/I4VXx2I is the inflection point, defining the applicability range of eq 1, which is tentatively below the Mott transition density. The parameter Vxx2 corresponds to higherorder (three-body) interactions, which have an opposite sign and strongly suppress the blueshift at large densities.18

This tendency is illustrated in Figure la, where linear scaling of AEmax with the exciton binding energy Eb can be clearly seen for the cases of both bulk excitons (green line) and 2D quantum well excitons (orange line). It should be noted that experimentally reported blueshifts are essentially smaller than the values given by this simple estimate. This is connected with practical problems of approaching the Mott transition limit without substantial heating of the sample and other undesired side effects. The observed values of polaritonic blueshift for various materials are summarized in Table 1. To our knowledge, the maximum values reached so far are about 13 meV, observed in microcavities with active media consisting of WS2 monolayers. Further details of the Coulomb-interaction-induced exciton blueshift in different systems are discussed in Sections 5.1—5.3 and Figure S8 in the Supporting Information.

The deviation from the discussed tendency is possible, if the electron—electron interaction differs substantially from the Coulomb law. One of the notorious examples of such materials are monolayer transition-metal dichalcogenides (TMD), where the dimensional reduction makes an exciton state different from that described by the hydrogen model.19 This results, among others, in a strong deviation (Figure 1a) of its nonlinear behavior from the general trend.3,20,21 Note, however, that from the point of view of excitonic nonlinearity the case of TMD monolayers is suboptimal, as the corresponding points lie below the line describing the case of the quantum wells of conventional semiconductors. Moreover, it is still challenging to find a way to boost the excitonic nonlinearity for 3D materials.

In turn, it is well-known that hybrid halide perovskites possess strong electron—phonon interactions, which are defined by high softness of their crystalline lattice22 (see Figure 1b). Moreover, excitons in these materials are characterized by a relatively high exciton binding energy and oscillator strength23 and high defect tolerance,24 which make perovskites highly attractive for studying room-temperature exciton-polariton dynamics and even Bose—Einstein con-

Nano Letters

pubs.acs.org/NanoLett

Table 1. Values of Experimentally Observed Blueshifts of Exciton-Polaritons in Various Materials, Including Conventional Semiconductors (GaAs, CdTe, GaN, ZnO), TMD Monolayers (MoSe2, WS2), Organic Materials (BODIPY-G1, MeLPPP, mCherry Protein), and Hybrid Perovskites ((PEA^Pb^, CsPbBr3, CsPbCl3, MAPM3)"

blueshift temperature

material group material (meV) (K) ref

semiconductor GaAs 0.6 8 31

QW 0.8 <10 32

2.2 <10 33

CdTe 1.8 19 7

ZnO 6.0 300 34

GaN 7.5 300 35

TMD MoSe2 3.0 127 21

5.0 7 3

WS2 1.0 300 36

13.0 300 37

polymers BODIPY-G1 6.0 300 38

MeLPPP 10.5 300 39

mCherry 12.1 300 40

perovskites (PEA)2PbI4 8.5 300 29

CsPbBr3 9.5 300 25

CsPbCl3 9.5 300 28

MAPbI3 13.0 170 this

work

MAPbI3 19.7 6 this

aThe previously reported maximum values of about 13 meV correspond to optical microcavities with active media consisting of WS2 monolayers. In this work we report the record high value of 19.7 meV for MAPM3 perovskites.

densation. An analysis of the corresponding nonlinearities thus seems to be an important task.

Here we present clear experimental evidence, supported by theoretical modeling, that exciton—phonon coupling leading to the formation of exciton-polarons in hybrid halide perovskites substantially modifies exciton—exciton interactions and allows a dramatic increase in the nonlinear optical response (Figure 1d), which is characterized by a record high value of the polariton blueshift up to 19.7 meV, remaining robust at elevated temperatures (170 K).

The big technological advantage of the use of halide perovskites for photonic applications41 is the variety of low-cost wet chemistry synthesis protocols to get high-quality thin films,42 for which additional nanostructuring can be routinely carried out by well-developed and efficient methods such as nanoimprint lithography.43 In particular, in order to achieve the strong exciton—photon coupling regime, instead of using vertical Bragg cavities to confine photons, one can realize a 1D photonic crystal slab by directly imprinting a CH3NH3PM3 (MAPM3) film. Since perovskites have a relatively high refractive index contrast with both air and the glass substrate («mapm3 ~ 2.2—2.5, nglass ~ 1.5), the well-localized leaky modes supported by the grating are characterized by local field enhancement, enabling their strong coupling with excitons possessing a high optical oscillator strength.

In the current work, thin and smooth films of MAPbI3 were fabricated by a spin-coating method in a nitrogen drybox.43 The obtained films were patterned by means of nanoimprint lithography using a periodic mold with a rectangular profile, as is schematically shown in Figure 1c. The resulting MAPbI3 photonic crystal slab is characterized by a thickness of 150 nm,

Figure 2. (a, b) Angle-resolved photoluminescence spectra of the patterned MAPM3 sample at 170 and 6 K. Dashed yellow lines correspond to uncoupled photon cavity mode dispersions. Dashed red lines correspond to uncoupled exciton levels, estimated from the fitting of LPBs by the coupled oscillator model. Green empty dots denote extracted polariton dispersions. Blue solid lines correspond to the polariton modes fitted with the coupled oscillator model. (c, d) Hopfield coefficients LXkl2 for excitonic (red lines) and ICkl2 for photonic (yellow lines) fractions in polaritons calculated from the coupled oscillator model.

Letter

Nano Letters

pubs.acs.org/NanoLett

Figure 3. (a, b) Angle-resolved reflectance spectra of a MAPbI3 sample at 170 and 6 K. Colored ellipses visualize angles and energies of the resonant laser pump in the nonlinear reflectance measurements. Red dashed squares visualize the respective areas shown in Figure 2a,b. (c, d) Evolution of the reflectance spectra, shown as solid blue lines, with the increase of incident pump fluence under resonant femtosecond excitation of LPB, corresponding to the blue ellipses in (a) and (b) for 170 and 6 K. Black dashed lines show Fano fits of the measured spectra. (e, f) Extracted LPB spectral blueshifts under femtosecond laser excitation as a function of incident pump fluence for 170 and 6 K. The corresponding theoretical calculations are shown with dashed lines. Inset tables show wavenumbers kx/ko of pumped polaritons. Dot colors correspond to the colors of the ellipses in (a) and (b). Horizontal error bars represent the RMS deviation of the pump laser fluence. Vertical error bars correspond to the standard deviation error obtained from Fano line shape fitting.

a period of ^period = 750 nm, a groove depth of 70 nm, and lateral fill factor off = d-idge/^period = 0.33 (see Section 1 in the Supporting Information).

To confirm the formation of exciton-polaritons, we performed angle-resolved photoluminescence (PL) spectroscopy measurements (see Methods) of the sample at T = 170 and 6 K (Figure 2a,b): i.e. above and below the temperature of the МАРЫ3 phase transition (~160 K) between tetragonal and orthorhombic phases, respectively.44,45 In both high-temperature tetragonal I4/mcm and low-temperature orthorhombic Pnma phases, МАРЫ3 exhibits a robust excitonic response, which manifests itself in the PL spectra as a broad-band angle-independent peak at energies of 1598 and 1655 meV, respectively. As well, in both phases, the TE-polarized photonic mode exhibits clear anticrossing with the corresponding exciton resonances. Fitting the dispersions of lower polariton branches (LPB) using the coupled oscillator model4 (Figure 2a,b) allowed us to estimate the Rabi splitting = 35.2 meV and coupling strength ^0 = 35.8 meV for the high-temperature tetragonal phase and = 35.7 meV and ^0 = 39.2 meV for the low-temperature orthorhombic phase (see Sections 2.1 and 2.2 in the Supporting Information for the details). The extracted Hopfield coefficients IXkl and ICkl representing, respectively, the angular dependence of excitonic and photonic fractions in the polaritons are shown in Figure2c,d. The estimated values of ^0 and for intermediate temperatures are described in Section 7.2 in the Supporting Information.

It is well-known that the linear excitonic response in organic—inorganic lead halide perovskites is strongly affected

by the polaron effects.47 49 It thus becomes interesting to investigate how the polaron effects will modify polariton nonlinearities. To do so, we measure the blueshifts of polariton branches in both crystal phases under resonant femtosecond-pulsed excitation depending on pump fluence and excitonic fraction in the polariton mode, defined by the angle of incidence (Figure 1d). In the experiment, the laser pump central frequencies and angles of incidence are chosen to resonantly probe each polariton branch with different excitonic fractions, as is shown in Figure 3a,b. In each measurement, the spectral position of the polariton mode is extracted using Fano line shape fitting of the reflectance spectrum obtained within the spectrum of the pulse (see Section 2.3 in the Supporting Information). Polariton mode spectra under a resonance pump with fitted Fano line shape at the lowest detuning for 170 and 6 K are shown in Figure 3c,d. The resulting fluence-dependent polariton mode blueshifts obtained at T = 170 and 6 K for various exciton fractions IXkI2 are shown in Figure 3e,f. The most pronounced blueshifts reaching ЛБ =13 meV for T = 170 K and ЛБ = 19.7 meV for T = 6 K are expectedly observed at smaller angles of incidence, corresponding to larger exciton fractions IXkI2. In both cases, the fluence dependence of the blueshifts is sublinear, clearly demonstrating effects of the saturation similar to those reported for TMD-based samples.18 A careful analysis of the line width of the polariton branch at T = 6 K reveals its broadening at k^/k0 ~ 0.31 (see Figure S5 in the Supporting Information). We assume this to be the exciton resonance corresponding to the tetragonal phase, which coexists with the orthorhombic Pnma phase at T = 6 K

Letter

Nano Letters

in the polycrystalline thin film and is weakly coupled to the photons.45,50 It gives rise to resonant absorption that leads to the reduction of the pump efficiency and, thus, the magnitude of polariton blueshifts observed for kx/ko = 0.329.

In order to unveil the physical origin of the observed fluence-dependent blueshift of the polariton spectrum, we develop a microscopic model of exciton-polariton response in the considered structure. Our model includes the quantum mechanical description of exciton-polaron state in MAPM3 perovskite, the calculation of excitonic nonlinearity rates, the quantitative description of polariton gas temporal dynamics, and the many-body renormalization of polariton resonance energy. As shown in Figure 3, the calculated spectrum demonstrates an excellent agreement with experimental data. We attribute the minor deviation observed for low excitonic fractions to the uncertainty in the estimation of the Hopfield coefficients (see Section 2 in the Supporting Information).

The excitonic properties of the considered material are strongly mediated by polaron effects, associated with coupling to the longitudinal optical phonon (LO) mode.48 Indeed, the static dielectric permittivity of MAPM3 is es = 25. In the 3D hydrogen-like model this corresponds to an exciton binding energy of about 3 meV, which makes excitons even less stable than in GaAs. In direct contradiction to this, we experimentally found the resonance energies of the exciton transition as Ex = 1598 meV in the tetragonal phase and Ex = 1655 meV at orthorhombic phase. This is in perfect agreement with previous measurements,47 where the corresponding exciton binding energies are reported to be E^ = 19 and 25 meV, respectively. Fixing the high-frequency dielectric permittivity to = 5 and altering the phonon energy, we reproduce these values within the Pollmann-Buttner model for exciton-polarons44,52 (see Sections 4.1 and 6 in the Supporting Information). The resulting Bohr radius is on the order of Ub ~ 2.5 nm.

The nonlinear optical response in the regime of strong light-matter coupling is governed by two effects. The first is a repulsive exciton-exciton exchange interaction, which shifts the position of the excitonic mode with an increase of the pump. The reduction of the Bohr radius due to the polaronic effects discussed above leads to a decrease of overlap of excitonic wavefunctions and thus to the reduction of exciton-exciton Coulomb interactions calculated within the Born approximation.17 On the other hand, the small radius of the excitons boosts the density of the Mott transition by 1-2 orders of magnitude as compared with conventional semiconductor materials, such as GaAs. In turn, this allows reaching the regime of elevated particle densities, where the strong interparticle interactions are quite pronounced and result in particular in potentially giant blueshifts (see Figure 1a). Thus, the polaron-induced gain in the particle density overcomes the polaron-induced reduction of the Kerr nonlinearity per particle. The second mechanism of polariton nonlinearity is associated with the composite quantum mechanical statistics of excitons, which leads to the saturation of the optical absorption and corresponding quenching of the Rabi splitting. This mechanism of optical nonlinearity is inherent for exciton-polaritons and is distinct from the nonlinear response emerging in the domain of other types of polaritons, such as the vibrational polaritons.53 55 We also note that the near-resonant excitation predominantly leads to the formation of exciton-polaritons, with negligible free carrier concentration.

Letter

Therefore, we neglect the other third-order nonlinear effects, related to the collective response of free carriers.56,57

Both mechanisms can be treated on an equal footing in the coupled oscillator model, which results in the following expression for the blueshift as a function of the wavevector-resolved polariton density «Lk, which can be estimated with use of the input—output formalism:

AELp(fc, nLl) « U(k)nLl- U2(k)nlk + O(«i) (2)

Here the expansion coefficients U(k) and ^(k) account for both Coulomb interactions and phase space filling effects and are calculated within the coboson formalism.18,58 Their expressions are given in Section 5.2 in the Supporting Information. We stress that the nonlinearity associated with the phase space filling scales as uB and under certain conditions is comparable with the Coulomb contribution (see Section 8 and Figure S13 in the Supporting Information). Notably, the quadratic in density term has an opposite sign as compared to the linear term, which leads to the saturation of the blueshift at elevated densities, as it is indeed in the experiment for both the tetragonal phase (Figure 3e) and the orthorhombic phase (Figure 3f). The comparison of exciton Coulomb-induced nonlinearity in the two phases and the temperature dependence is presented in Sections 6 and 7.1 in the Supporting Information, and the results are summarized in Figures S9 and S10. In both cases, the reduction of the blueshift with the growth of the wavevector illustrated by Figure 3a,b is caused by the corresponding reduction ofthe exciton fraction (see Figure 2c,d). For the orthorhombic phase we report additional suppression of the blueshift observed at intermediate values of the wavevector (red and olive dots in Figure 3f). We attribute this effect to the residual fraction of the tetragonal phase, having an exciton with reduced oscillator strength lying about 50 meV lower in energy. The presence of this exciton plays a parasitic role, as it becomes unintentionally excited when pumping near its resonance. Further details of the theoretical treatment are given in Section 4 in the Supporting Information.

In summary, we have demonstrated the formation of the robust nonlinear polariton response in the patterned bulk hybrid halide perovskite slabs. It has been shown that polaronic effects stemming from strong exciton-phonon interactions dramatically increase the stability of the excitons in perovskites and enhance the corresponding nonlinear optical properties. A record high value of 19.7 meV for the polariton blueshift, which is about 50% higher than the values for other materials, has been reported. The experimental data are in good quantitative agreement with the results of the microscopic theoretical treatment. The observed polaronic enhancement of the polariton nonlinear blueshift can be directly expanded to the room-temperature domain for the MAPbBr3 material, supporting a robust exciton-polaron response at room temperature. Large values of blueshift allow for the realization of deeper nonlinear potential profiles for polaritons by means of a spatially inhomogeneous pump. Moreover, since the observed blueshifts are almost equal to the polariton line width, this allows for the realization of nonlinear polariton switches based on perovskite structures. Our research opens the route to further exploration of the phonon-mediated polariton interactions for future energy-efficient and thermally stable polaritonic devices.

pubs.acs.org/NanoLett

Nano Letters

■ METHODS

Sample Fabrication. The МАРЫ3 thin film was synthesized by a solvent engineering method.60 A solution of the perovskite was prepared in a nitrogen drybox in the following way: 79.5 mg of methylammonium iodide (MAI) from GreatCell Solar and 230.5 mg of lead(II) iodide (РЫ2) from TCI was dissolved in 1 mL of a DMF/DMSO solvent mixture in the ratio 9/1. The resulting 0.5 M solution of МАРЫ3 was stirred for 1 day at 27 °C. Film fabrication was performed in a nitrogen drybox by a spin-coating method. SiO2 substrates (25 X 25 mm) were washed consecutively with sonication in deionized water, acetone, and 2-propanol for 10 min and afterward cleaned in an oxygen plasma cleaner for 15 min. The perovskite solution (40 fL) was deposited on the substrate and spin-coated in one step at 4000 rpm for 40 s. At 11s 500 ffL of toluene was dripped on top of the rotating substrate. The substrate with MAPbI3 at the intermediate phase was placed under vacuum for 3 min at room temperature to evaporate the residues of the solvents and toluene. The resulting thin film was structured by a nanoimprint lithography method.61 We used a DVD disk grating with a period of 750 nm, a 120 nm ridge height, and a fill factor (dridge/dperiod) of 0.67 as a mold. The mold was cleaned in methanol and deionized water and then dried before the imprinting. The imprint process was carried out under 4.8 MPa for 10 min after the mold was removed. As the adhesion of SiO2 substrates was quite large after the plasma cleaning, no antiadhesive layer was needed. Imprinted perovskite samples were annealed at 100 °C for 10 min. After the nanoimprint process was finished, a perovskite nanograting was formed with negative replication of the DVD disk mold used.

Optical Measurements. Angle-resolved reflectance spec-troscopy was performed using a back-focal-plane imaging setup with a slit spectrometer coupled to a liquid-nitrogen-cooled imaging CCD camera (Princeton Instruments SP2500+Py-LoN) and a halogen lamp employed for white-light illumination. Angle-resolved PL measurements were performed in the same setup with off-resonant excitation by monochromatic light from a femtosecond (fs) laser (Pharos, Light Conversion) coupled with a broad-bandwidth optical parametric amplifier (Orpheus-F, Light Conversion) and compressor at a wavelength of 680 nm, 40 fs pulse duration, and 100 kHz repetition rate. The pulsed regime at 100 kHz was confirmed by the measurements at 1 kHz (see Section 3 in the Supporting Information for details). For pump-dependent reflectivity measurements, the sample was excited by 40 fs pulses from the same wavelength-tunable laser. The angle of incidence was controlled via focusing of the laser beam within the back focal plane of the objective lens. The sample was mounted in an ultralow-vibration closed-cycle helium cryostat (Advanced Research Systems) and maintained at a controllable temperature in the range of 7—300 K. The cryostat was mounted onto a precise XYZ stage for sample positioning. Spatial filtering in the detection channel was used to avoid parasitic signals originating from the reflections from the optical elements of the setup. More details on the experimental scheme are provided in Figure S4 in the Supporting Information.

Theory. A detailed description of theoretical modeling is presented in Sections 4—8 in the Supporting Information.

Letter

■ ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.2c03524.

Characterization of the sample, SEM, AFM and angle-resolved spectroscopy at room temperature, extraction of the uncoupled cavity photon mode dispersion, influence of thermal effects on the blueshift measurements, theory of exciton-polariton nonlinearity, phonon energy dependence of exciton Coulomb nonlinearity, temperature dependence of exciton Coulomb non-linearity and light—matter coupling strength, and polariton nonlinearity rates (PDF)

■ AUTHOR INFORMATION Corresponding Author

Anton K. Samusev — ITMO University, School of Physics and Engineering, St. Petersburg 197101, Russia; Experimentelle Physik 2, Technische Universität Dortmund, 44227 Dortmund, Germany; В orcid.org/0000-0002-3547-6573; Email: [e-mail]

Authors

Mikhail A. Masharin — ITMO University, School of Physics and Engineering, St. Petersburg 197101, Russia; © orcid.org/0000-0003-0687-8706 Vanik A. Shahnazaryan — ITMO University, School of Physics and Engineering, St. Petersburg 197101, Russia; ©orcid.org/0000-0001-7892-0550 Fedor A. Benimetskiy — ITMO University, School of Physics and Engineering, St. Petersburg 197101, Russia; ® orcid.org/0000-0003-3320-0554 Dmitry N. Krizhanovskii — Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom; Q orcid.org/0000-0002-6436-7384 Ivan A. Shelykh — ITMO University, School of Physics and Engineering, St. Petersburg 197101, Russia; Science Institute, University of Iceland, IS-107 Reykjavik, Iceland; ©orcid.org/0000-0001-5393-821X Ivan V. Iorsh — ITMO University, School of Physics and Engineering, St. Petersburg 197101, Russia; Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel; © orcid.org/0000-0003-4992-6122 Sergey V. Makarov — ITMO University, School of Physics and Engineering, St. Petersburg 197101, Russia; Qingdao Innovation and Development Center, Harbin Engineering University, Qingdao 266000 Shandong, China; orcid.org/ 0000-0002-9257-6183

Complete contact information is available at: https://pubs.acs.org/10.1021/acs.nanolett.2c03524

Author Contributions

M.A.M. and V.A.S. contributed equally to this work. Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The experimental part of this work carried out by M.A.M. and F.A.B. was funded by the Russian Science Foundation, grant #21-12-00218. Sample fabrication by M.A.M. was supported by the Ministry of Science and Higher Education of the Russian Federation (Project 075-15-2021-589). VAS., IAS.,

pubs.acs.org/NanoLett

Nano Letters

and I.V.I. are responsible for the theoretical part of the work and acknowledge Priority 2030 Federal Academic Leadership Program. IA.S. acknowledges the support of the Icelandic Research Fund (Rannis), project No. 163082-051. A.K.S. acknowledges the Mercur Foundation (Grant Pe-2019-0022) and TU Dortmund core funds.

■ REFERENCES

(1) Weisbuch, C.; Nishioka, M.; Ishikawa, A.; Arakawa, Y. Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity. Phys. Rev. Lett. 1992, 69, 3314.

(2) Ciers, J.; Roch, J. G.; Carlin, J.-F.; Jacopin, G.; Butté, R.; Grandjean, N. Propagating Polaritons in III-Nitride Slab Waveguides. Phys. Rev. Applied 2017, 7, 034019.

(3) Kravtsov, V.; Khestanova, E.; Benimetskiy, F. A.; Ivanova, T.; Samusev, A. K.; Sinev, I. S.; Pidgayko, D.; Mozharov, A. M.; Mukhin, I. S.; Lozhkin, M. S.; et al. Nonlinear polaritons in a monolayer semiconductor coupled to optical bound states in the continuum. Light: Science & Applications 2020, 9, 1-8.

(4) Gogna, R.; Zhang, L.; Wang, Z.; Deng, H. Photonic crystals for controlling strong coupling in van der Waals materials. Opt. Express 2019, 27, 22700-22707.

(5) Carusotto, I.; Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 2013, 85, 299-366.

(6) Liew, T. C. H.; Shelykh, I. A.; Malpuech, G. Polariton devces. PhysicaE 2011, 43, 1543.

(7) Kasprzak, J.; Richard, M.; Kundermann, S.; Baas, A.; Jeambrun, P.; Keeling, J. M. J.; Marchetti, F.; Szymanska, M.; André, R.; Staehli, J.; et al. Bose-Einstein condensation of exciton polaritons. Nature 2006, 443, 409-414.

(8) Bajoni, D.; Senellart, P.; Wertz, E.; Sagnes, I.; Miard, A.; Lemaître, A.; Bloch, J. Polariton laser using single micropillar GaAs-GaAlAs semiconductor cavities. Physical review letters 2008, 100, 047401.

(9) Gao, T.; Eldridge, P.; Liew, T. C. H.; Tsintzos, S.; Stavrinidis, G.; Deligeorgis, G.; Hatzopoulos, Z.; Savvidis, P. Polariton condensate transistor switch. Phys. Rev. B 2012, 85, 235102.

(10) Nguyen, H. S.; Vishnevsky, D.; Sturm, C.; Tanese, D.; Solnyshkov, D.; Galopin, E.; Lemaître, A.; Sagnes, I.; Amo, A.; Malpuech, G.; et al. Realization of a double-barrier resonant tunneling diode for cavity polaritons. Phys. Rev. Lett. 2013, 110, 236601.

(11) Sturm, C.; Tanese, D.; Nguyen, H.; Flayac, H.; Galopin, E.; Lemaître, A.; Sagnes, I.; Solnyshkov, D.; Amo, A.; Malpuech, G.; et al. All-optical phase modulation in a cavity-polariton Mach-Zehnder interferometer. Nat. Commun. 2014, 5, 1-7.

(12) Semond, F.; Sellers, I.; Natali, F.; Byrne, D.; Leroux, M.; Massies, J.; Ollier, N.; Leymarie, J.; Disseix, P.; Vasson, A. Strong light-matter coupling at room temperature in simple geometry GaN microcavities grown on silicon. Appl. Phys. Lett. 2005, 87, 021102.

(13) Marsault, F.; Nguyen, H. S.; Tanese, D.; Lemaître, A.; Galopin, E.; Sagnes, I.; Amo, A.; Bloch, J. Realization of an all optical exciton-polariton router. Appl. Phys. Lett. 2015, 107, 201115.

(14) Liu, X.; Galfsky, T.; Sun, Z.; Xia, F.; Lin, E.-c.; Lee, Y.-H.; Kéna-Cohen, S.; Menon, V. M. Strong light-matter coupling in two-dimensional atomic crystals. Nat. Photonics 2015, 9, 30-34.

(15) van Vugt, L. K.; Ruhle, S.; Ravindran, P.; Gerritsen, H. C.; Kuipers, L.; Vanmaekelbergh, D. Exciton polaritons confined in a ZnO nanowire cavity. Physical review letters 2006, 97, 147401.

(16) Li, F.; Orosz, L.; Kamoun, O.; Bouchoule, S.; Brimont, C.; Disseix, P.; Guillet, T.; Lafosse, X.; Leroux, M.; Leymarie, J.; et al. From excitonic to photonic polariton condensate in a ZnO-based microcavity. Physical review letters 2013, 110, 196406.

(17) Ciuti, C.; Savona, V.; Piermarocchi, C.; Quattropani, A.; Schwendimann, P. Role of the exchange of carriers in elastic exciton-exciton scattering in quantum wells. Phys. Rev. B 1998, 58, 7926.

(18) Emmanuele, R.; Sich, M.; Kyriienko, O.; Shahnazaryan, V.; Withers, F.; Catanzaro, A.; Walker, P.; Benimetskiy, F.; Skolnick, M.;

Letter

Tartakovskii, A.; et al. Highly nonlinear trion-polaritons in a monolayer semiconductor. Nat. Commun. 2020, 11, 1-7.

(19) Chernikov, A.; Berkelbach, T. C.; Hill, H. M.; Rigosi, A.; Li, Y.; Aslan, O. B.; Reichman, D. R.; Hybertsen, M. S.; Heinz, T. F. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS 2. Physical review letters 2014, 113, 076802.

(20) Shahnazaryan, V.; Iorsh, I.; Shelykh, I. A.; Kyriienko, O. Exciton-exciton interaction in transition-metal dichalcogenide mono-layers. Phys. Rev. B 2017, 96, 115409.

(21) Stepanov, P.; Vashisht, A.; Klaas, M.; Lundt, N.; Tongay, S.; Blei, M.; Höfling, S.; Volz, T.; Minguzzi, A.; Renard, J.; et al. Exciton-exciton interaction beyond the hydrogenic picture in a MoSe 2 monolayer in the strong light-matter coupling regime. Phys. Rev. Lett. 2021, 126, 167401.

(22) Wright, A. D.; Verdi, C.; Milot, R. L.; Eperon, G. E.; Pérez-Osorio, M. A.; Snaith, H. J.; Giustino, F.; Johnston, M. B.; Herz, L. M. Electron-phonon coupling in hybrid lead halide perovskites. Nat. Commun. 2016, 7, 1-9.

(23) Su, R.; Fieramosca, A.; Zhang, Q.; Nguyen, H. S.; Deleporte, E.; Chen, Z.; Sanvitto, D.; Liew, T. C.; Xiong, Q. Perovskite semiconductors for room-temperature exciton-polaritonics. Nat. Mater. 2021, 20, 1315-1324.

(24) Huang, H.; Bodnarchuk, M. I.; Kershaw, S. V.; Kovalenko, M. V.; Rogach, A. L. Lead halide perovskite nanocrystals in the research spotlight: stability and defect tolerance. ACS energy letters 2017, 2, 2071-2083.

(25) Su, R.; Wang, J.; Zhao, J.; Xing, J.; Zhao, W.; Diederichs, C.; Liew, T. C.; Xiong, Q. Room temperature long-range coherent exciton polariton condensate flow in lead halide perovskites. Science advances 2018, 4, eaau0244.

(26) Su, R.; Ghosh, S.; Wang, J.; Liu, S.; Diederichs, C.; Liew, T. C.; Xiong, Q. Observation of exciton polariton condensation in a perovskite lattice at room temperature. Nat. Phys. 2020, 16, 301-306.

(27) Feng, J.; Wang, J.; Fieramosca, A.; Bao, R.; Zhao, J.; Su, R.; Peng, Y.; Liew, T. C.; Sanvitto, D.; Xiong, Q. All-optical switching based on interacting exciton polaritons in self-assembled perovskite microwires. Science Advances 2021, 7, eabj6627.

(28) Su, R.; Diederichs, C.; Wang, J.; Liew, T. C.; Zhao, J.; Liu, S.; Xu, W.; Chen, Z.; Xiong, Q. Room-temperature polariton lasing in all-inorganic perovskite nanoplatelets. Nano Lett. 2017, 17, 3982-3988.

(29) Fieramosca, A.; Polimeno, L.; Ardizzone, V.; De Marco, L.; Pugliese, M.; Maiorano, V.; De Giorgi, M.; Dominici, L.; Gigli, G.; Gerace, D.; et al. Two-dimensional hybrid perovskites sustaining strong polariton interactions at room temperature. Science advances 2019, 5, eaav9967.

(30) Bouteyre, P.; Nguyen, H. S.; Lauret, J.-S.; Trippé-Allard, G.; Delport, G.; Lédée, F.; Diab, H.; Belarouci, A.; Seassal, C.; Garrot, D.; et al. Room-temperature cavity polaritons with 3D hybrid perovskite: toward large-surface polaritonic devices. ACS photonics 2019, 6, 1804-1811.

(31) Brichkin, A.; Novikov, S.; Larionov, A.; Kulakovskii, V.; Glazov, M.; Schneider, C.; Höfling, S.; Kamp, M.; Forchel, A. Effect of Coulomb interaction on exciton-polariton condensates in GaAs pillar microcavities. Phys. Rev. B 2011, 84, 195301.

(32) Mukherjee, S.; Myers, D. M.; Lena, R. G.; Ozden, B.; Beaumariage, J.; Sun, Z.; Steger, M.; Pfeiffer, L. N.; West, K.; Daley, A. J.; et al. Observation ofnonequilibrium motion and equilibration in polariton rings. Phys. Rev. B 2019, 100, 245304.

(33) Estrecho, E.; Gao, T.; Bobrovska, N.; Comber-Todd, D.; Fraser, M. D.; Steger, M.; West, K.; Pfeiffer, L. N.; Levinsen, J.; Parish, M.; et al. Direct measurement of polariton-polariton interaction strength in the Thomas-Fermi regime of exciton-polariton condensation. Phys. Rev. B 2019, 100, 035306.

(34) Li, F.; Orosz, L.; Kamoun, O.; Bouchoule, S.; Brimont, C.; Disseix, P.; Guillet, T.; Lafosse, X.; Leroux, M.; Leymarie, J.; et al. Fabrication and characterization of a room-temperature ZnO polariton laser. Appl. Phys. Lett. 2013, 102, 191118.

(35) Christopoulos, S.; Von Högersthal, G. B. H.; Grundy, A.; Lagoudakis, P.; Kavokin, A.; Baumberg, J.; Christmann, G.; Butté, R.;

pubs.acs.org/NanoLett

Nano Letters

Feltin, E.; Carlin, J.-F.; et al. Room-temperature polariton lasing in semiconductor microcavities. Physical review letters 2007, 98, 126405.

(36) Zhao, J.; Su, R.; Fieramosca, A.; Zhao, W.; Du, W.; Liu, X.; Diederichs, C.; Sanvitto, D.; Liew, T. C.; Xiong, Q. Ultralow threshold polariton condensate in a monolayer semiconductor microcavity at room temperature. Nano Lett. 2021, 21, 3331—3339.

(37) Barachati, F.; Fieramosca, A.; Hafezian, S.; Gu, J.; Chakraborty, B.; Ballarini, D.; Martinu, L.; Menon, V.; Sanvitto, D.; Kéna-Cohen, S. Interacting polariton fluids in a monolayer of tungsten disulfide. Nature Nanotechnol. 2018, 13, 906—909.

(38) Yagafarov, T.; Sannikov, D.; Zasedatelev, A.; Georgiou, K.; Baranikov, A.; Kyriienko, O.; Shelykh, I.; Gai, L.; Shen, Z.; Lidzey, D.; et al. Mechanisms of blueshifts in organic polariton condensates. Communications Physics 2020, 3, 1—10.

(39) Zasedatelev, A. V.; Baranikov, A. V.; Urbonas, D.; Scafirimuto, F.; Scherf, U.; Stöferle, T.; Mahrt, R. F.; Lagoudakis, P. G. A room-temperature organic polariton transistor. Nat. Photonics 2019, 13, 378—383.

(40) Betzold, S.; Dusel, M.; Kyriienko, O.; Dietrich, C. P.; Klembt, S.; Ohmer, J.; Fischer, U.; Shelykh, I. A.; Schneider, C.; Hofling, S. Coherence and Interaction in confined room-temperature polariton condensates with Frenkel excitons. ACS Photonics 2020, 7, 384—392.

(41) Sutherland, B. R.; Sargent, E. H. Perovskite photonic sources. Nat. Photonics 2016, 10, 295—302.

(42) Dunlap-Shohl, W. A.; Zhou, Y.; Padture, N. P.; Mitzi, D. B. Synthetic approaches for halide perovskite thin films. Chem. Rev. 2019, 119, 3193—3295.

(43) Makarov, S. V.; Milichko, V.; Ushakova, E. V.; Omelyanovich, M.; Cerdan Pasaran, A.; Haroldson, R.; Balachandran, B.; Wang, H.; Hu, W.; Kivshar, Y. S.; et al. Multifold emission enhancement in nanoimprinted hybrid perovskite metasurfaces. ACS Photonics 2017, 4, 728—735.

(44) Menéndez-Proupin, E.; Beltran Rios, C. L.; Wahnon, P. Nonhydrogenic exciton spectrum in perovskite CH3NH3PbI3. physica status solidi (RRL)-Rapid Research Letters 2015, 9, 559—563.

(45) Lee, K. J.; Turedi, B.; Giugni, A.; Lintangpradipto, M. N.; Zhumekenov, A. A.; Alsalloum, A. Y.; Min, J.-H.; Dursun, I.; Naphade, R.; Mitra, S.; et al. Domain-Size-Dependent Residual Stress Governs the Phase-Transition and Photoluminescence Behavior of Methylammonium Lead Iodide. Adv. Funct. Mater. 2021, 31, 2008088.

(46) Hopfield, J. Theory of the contribution of excitons to the complex dielectric constant of crystals. Phys. Rev. 1958, 112, 1555.

(47) Soufiani, A. M.; Huang, F.; Reece, P.; Sheng, R.; Ho-Baillie, A.; Green, M. A. Polaronic exciton binding energy in iodide and bromide organic-inorganic lead halide perovskites. Appl. Phys. Lett. 2015, 107, 231902.

(48) Baranowski, M.; Plochocka, P. Excitons in metal-halide perovskites. Adv. Energy Mater. 2020, 10, 1903659.

(49) Buizza, L. R.; Herz, L. M. Polarons and Charge Localization in Metal-Halide Semiconductors for Photovoltaic and Light-Emitting Devices. Adv. Mater. 2021, 33, 2007057.

(50) Phuong, L. Q.; Yamada, Y.; Nagai, M.; Maruyama, N.; Wakamiya, A.; Kanemitsu, Y. Free carriers versus excitons in CH3NH3PbI3 perovskite thin films at low temperatures: charge transfer from the orthorhombic phase to the tetragonal phase. journal of physical chemistry letters 2016, 7, 2316—2321.

(51) Gelmetti, I.; Cabau, L.; Montcada, N. F.; Palomares, E. Selective organic contacts for methyl ammonium lead iodide (MAPI) perovskite solar cells: influence of layer thickness on carriers extraction and carriers lifetime. ACS Appl. Mater. Interfaces 2017, 9, 21599—21605.

(52) Pollmann, J.; Buttner, H. Effective Hamiltonians and bindings energies of Wannier excitons in polar semiconductors. Phys. Rev. B 1977, 16, 4480.

(53) Ribeiro, R. F.; Dunkelberger, A. D.; Xiang, B.; Xiong, W.; Simpkins, B. S.; Owrutsky, J. C.; Yuen-Zhou, J. Theory for nonlinear spectroscopy of vibrational polaritons. journal of physical chemistry letters 2018, 9, 3766—3771.

Letter

(54) Ribeiro, R. F.; Martínez-Martínez, L. A.; Du, M.; Campos-Gonzalez-Angulo, J.; Yuen-Zhou, J. Polariton chemistry: controlling molecular dynamics with optical cavities. Chemical science 2018, 9, 6325-6339.

(55) Ribeiro, R. F.; Campos-Gonzalez-Angulo, J. A.; Giebink, N. C.; Xiong, W.; Yuen-Zhou, J. Enhanced optical nonlinearities under collective strong light-matter coupling. Phys. Rev. A 2021, 103, 063111.

(56) Kalanoor, B. S.; Gouda, L.; Gottesman, R.; Tirosh, S.; Haltzi, E.; Zaban, A.; Tischler, Y. R. Third-order optical nonlinearities in organometallic methylammonium lead iodide perovskite thin films. Acs Photonics 2016, 3, 361-370.

(57) Ferrando, A.; Martinez Pastor, J. P.; Suarez, I. Toward metal halide perovskite nonlinear photonics. J. Phys. Chem. Lett. 2018, 9, 5612-5623.

(58) Combescot, M.; Betbeder-Matibet, O.; Dubin, F. The many-body physics of composite bosons. Phys. Rep. 2008, 463, 215 - 320.

(59) Shi, J.; Li, Y.; Wu, J.; Wu, H.; Luo, Y.; Li, D.; Jasieniak, J. J.; Meng, Q. Exciton Character and High-Performance Stimulated Emission of Hybrid Lead Bromide Perovskite Polycrystalline Film. Advanced Optical Materials 2020, 8, 1902026.

(60) Jeon, N.J.; Noh,J. H.; Kim, Y. C.; Yang, W. S.; Ryu, S.; Seok, S. I. Solvent engineering for high-performance inorganic-organic hybrid perovskite solar cells. Nature materials 2014, 13, 897-903.

(61) Tiguntseva, E.; Sadrieva, Z.; Stroganov, B.; Kapitonov, Y. V.; Komissarenko, F.; Haroldson, R.; Balachandran, B.; Hu, W.; Gu, Q.; Zakhidov, A.; et al. Enhanced temperature-tunable narrow-band photoluminescence from resonant perovskite nanograting. Appl. Surf. Sci. 2019, 473, 419-424.

Recommended by ACS

Large Exciton Polaron Formation in 2D Hybrid Perovskites via Time-Resolved Photoluminescence

Sebastian Hurtado Parra, James M. Kikkawa, et al. december 15,2022

acs nano READ [2f

Revealing Giant Exciton Fine-Structure Splitting in Two-Dimensional Perovskites Using van der Waals Passivation

Rodolfo Canet-Albiach, Guillermo Mufioz-Matutano, et a!. september 08, 2022

nano letters READ CT

Hot Phonon Bottleneck Stimulates Giant Optical Gain in Lead Halide Perovskite Quantum Dots

Zhonghui Nie, Yue Wang, et al. september 29, 2022

acs photonics READ

Strain Tuning Self-Assembled Quantum Dots for Energy-Tunable Entangled-Photon Sources Using a Photolithographically Fabricated Microelectromechanical...

Weiwen Ou, Jiaxiang Zhang, et al. september 23, 2022

acs photonics READ

Get More Suggestions >

pubs.acs.org/NanoLett

Pnotonics

pubs.acs.org/journal/apchd5

Room-Temperature Polaron-Mediated Polariton Nonlinearity in MAPbBr3 Perovskites

Mikhail A. Masharin,# Vanik A. Shahnazaryan,*'# Ivan V. Iorsh, Sergey V. Makarov, Anton IK Samusev, and Ivan A. Shelykh

Cite This: ACS Photonics 2023, 10, 691-698

Read Online

ACCESS

lilil Metrics & More

IÜ Article Recommendations

[s^ Supporting Information

Angle-resolved PL

Polariton blueshift

a =

H ^

¡D o

m w

c^ >>

Resonant pump

\

ABSTRACT: Systems supporting exciton-polaritons represent solid-state optical platforms with a strong built-in optical nonlinearity provided by exciton-exciton interactions. In conventional semiconductors, with hydrogen-like excitons, the non-linearity rate demonstrates the inverse scaling with the binding energy. This makes excitons that are stable at room temperature weakly interacting, which obviously limits the possibilities of practical applications of the corresponding materials for nonlinear photonics. We demonstrate, experimentally and theoretically, that these limitations can be substantially softened in hybrid perov-skites, such as MAPbBr3, due to the crucial role of the polaron

effects mediating the interparticle interactions. The resulting exciton-polaron-polaritons remain both stable and strongly interacting at room temperature, which is confirmed by large nonlinear blueshifts of lower polariton branch energy under resonant femtosecond laser pulse excitation. Our findings open novel perspectives for the management of the exciton-polariton nonlinearities in ambient conditions.

KEYWORDS: exciton-polariton, polariton nonlinear blueshift, photonic crystal slab, polaron, exciton-polaron model, halide perovskites

200 400 600 Fluence, pj/cm2

d '3

m M K M

■ INTRODUCTION

Excitons are bound states of an electron in a conduction band and a hole in a valence band that are being held together due to the Coulomb attraction. In direct bandgap materials they can be created by the absorption of photons and annihilated with photon emission. In specific designs, when a material with an optical excitonic transition is embedded inside an optical cavity and the energies of a cavity mode and excitonic transition are brought close to resonance, the regime of strong light—matter coupling can be achieved.1 This happens when the characteristic coupling strength, defined by the optical dipole moment of the excitonic transition, exceeds all characteristic broadenings. Strong coupling has been demonstrated for a variety of experimental geometries, including planar Bragg microcavities,2 planar waveguides,3 or photonic crystal slabs supporting photonic bound states in continuum (BIC) and leaky modes.4,5

Hybridization between excitons and cavity photons results in the appearance of a new type of composite elementary excitations in the system, known as exciton-polaritons. The combination of the extremely small effective mass of the polaritons (about 5 orders of magnitude smaller compared to the free electron mass) with a macroscopically large coherence length6 and the strong nonlinear optical response provided by exciton—exciton interactions7,8 make polariton systems attractive candidates for the realization of the nonlinear optical

elements of a new generation,9 including extra low threshold lasers10 and all-optical integrated circuits.11-14 Moreover, polaritons present an ideal platform for the study of collective quantum phenomena at surprisingly high temperatures.15

However, for the practical applications of polaritonics, there is still a lack of the material base. Indeed, the use of structures with quantum wells based on conventional semiconductor materials, such as GaAs16,17 and CdTe10 are limited to cryogenic temperatures. On the other hand, the production of high-quality samples based on wide-gap materials such as GaN1 ,19 or ZnO20 require expensive fabrication methods, transition metal dichalcogenide-based systems5,21 (TMDs) are difficult to scale up, and polymer materials (MeLPPP,22 mCherry23) are highly disordered and are still mostly used in bulky vertical Bragg cavities, which are barely compatible with on-chip designs. Moreover, as all these materials possess tightly bound excitons, it means that the exciton—exciton interaction and, consequently, the nonlinear optical coefficient are substantially reduced.

Received: November 13, 2022 Published: February 14, 2023

ACS Publications

© 2023 American Chemical Society

Article

691

ACS Photonics

pubs.acs.org/journal/apchd5

Figure 1. (a) Concept image of a 1D MAPbB^ PCS fabrication by nanoimprint lithography. In a thin film of MAPbB^ excitonic transition is strongly coupled with a waveguide photonic mode, which lies below the light cone. The presence of the periodic grating leads to the transformation of the photonic waveguide modes into leaky PCS modes, which makes possible direct optical excitation and detection of the polaritons (b) The morphology of the fabricated 1D MAPbBr3 PCS measured by the AFM method. The color corresponds to the height in each point of the sample from low (dark colors) to high (light colors). (c) The horizontal profile of the studied sample obtained from the AFM measurement. The data show the presence of accurate ridges with a height of about 100 nm. (d) Image of the studied sample, made by SEM, which shows the grating period of 750 nm and the ridge width of 200 nm. (e) Measured angle-resolved reflectance spectrum of fabricated MAPbBr3 PCS in TE polarization, which shows the dispersion of the leaky modes supported by the PCS. The wavevector of light in free space k is defined as k = E/(h*c), where E is the photon energy and c is the speed of light. The curvature of the mode near the 2.3 eV is attributed to the coupling with the excitonic resonance. In the spectral region above 2.3 eV, there is no photonic mode due to the high optical absorption. (f) The simulated angle-resolved spectrum of the studied structure obtained using the FMM. The results are in good agreement with the experimental data.

In this context, halide perovskites are very promising candidates for the practical applications of polaritonics. This is due to the combination of their remarkable properties, namely, stability of excitons at room temperature, high optical oscillator strength of the excitonic transitions, defect tolerance, availability of well developed and cheap fabrication and nanostructuring and simple scaling-up technologies,24,25 and the ability to support high-Q optical modes at the nanoscale due to the high refractive index of the material.26 The latter allows the realization of a planar optical cavity in the geometry of a photonic crystal slab (PCS) made directly from the active excitonic material with high localization of the optical field and thus an enhanced light—matter interaction. Moreover, it is well-known that due to the polar nature of their crystalline lattice, hybrid halide perovskites possess a strong electron— phonon interaction,27 which leads to the substantial enhancement of their optical nonlinear properties, as we will show below.

The nonlinear optical response of exciton-polaritons is determined by their excitonic component and can be experimentally detected as a blueshift of the lower polariton line with an increase in the intensity of the external pump. This phenomenon is mainly due to the two mechanisms. The first one is related to the exciton—exciton interactions, for which exchange contribution is dominant7,8 and which observatio-nally increases with an increase of the exciton concentration. The second one is connected with the saturation of the optical absorption related to the composite quantum statistics of excitons and results in the quenching of the Rabi splitting. The combination of these two effects allows the successful use of polariton systems in nonlinear photonic devices28 with characteristic response times up to the subpicosecond range29 with perovskites being one of the promising material platforms. Polariton nonlinearity has been already demonstrated experimentally in all-inorganic and so-called quasi-2D

perovskites,24,30,31 but the corresponding properties of hybrid organic-inorganic perovskites (HOIPs) were not yet investigated. Hybrid perovskites possess certain important differences from all-inorganic perovskites, such as a soft polar crystal lattice favorable for polaron formation.32 Importantly, polaron effects can be expected to modify the interaction potential,33 which leads to the enhancement of the exciton binding energy and substantial increase of the polariton nonlinear response. 4

Among HOIPs, bromide-based perovskite MAPbBr3 is a perspective material for room-temperature polaritonics, since it has an exciton with sufficiently high binding energy and high oscillator strength, stable even in the polycrystalline phase.33,35 Previously, a strong light-matter coupling regime was reported in MAPbBr3 nanowires36 and thin films embedded in vertical Bragg cavities.37 Polariton optical nonlinearity was not studied in both mentioned geometries so far, but was investigated in the related material MAPb^,34 where record high values of the polariton blueshift (up to 19.7 meV) were reported. However, relatively low exciton binding energy in MAPb^ makes the observed effect possible only at cryogenic temperatures. This obviously limits the possibility of the practical applications, and the study of the nonlinear response of MAPbBr3 thus represents an important contribution in the field.

In this work, we use MAPbBr3 thin film as an active medium with room-temperature stable excitons. We structure the film using a nanoimprint lithography method with a periodic grating mold to get a photonic crystal slab (PCS). We demonstrate that in this geometry the coupling of an excitonic transition with leaky modes of the PCS results in the formation of robust exciton-polaritons. We study experimentally the temperature dependence of the properties of this system and demonstrate, among the rest, the pronounced nonlinear polariton response at room temperature. Moreover, we present a theoretical model that reveals the main mechanisms of the polariton nonlinearity and gives a quantitative description of

Article

ACS Photonics

pubs.acs.org/journal/apchd5

Figure 2. (a) Measured angle-resolved PL spectra at different temperatures under nonresonant pump. The color corresponds to the intensity of the emitted light. The data contain the background emission over all kx/k*0 and emission of the leaky modes in the strong coupling regime. The dashed orange lines correspond to the uncoupled cavity photon mode, red dashed lines correspond to the exciton levels, and the green solid lines describe the lower polariton branches, obtained by coupled oscillator model optimization. The observed shift of the lower polariton mode with temperature is attributed with the shift of the excitonic level. (b) Extracted Hopfield coefficients as functions of kx/k for the given temperatures, estimated from the results of coupled oscillator model optimization. Orange and red lines correspond to the photon (ICkl2) and exciton (l-X^2) fractions, respectively. (c, d) Extracted values of the excitonic energy E- in MAPbBr3 PCS and light—matter coupling coefficient ¿0 as functions of the temperature. The redshift of the exciton level with lowering the temperature is attributed to the polaron effects. The rise of ¿0 at low temperatures is affiliated with the enhancement of the excitonic response42 and lowering of the nonradiative losses.

Article

the experimental data. Potential perspectives of MAPbB^ in exciton-polariton applications are also highlighted.

■ METHODS

Sample Fabrication. The fabrication of the perovskite PCS (see Figure 1a) consists of two steps: the synthesis of the MAPbBr3 thin film followed by the nanoimprint lithography.

First, a thin MAPbBr3 film is synthesized by the solvent engineering method.38 Perovskite solution is prepared in a nitrogen drybox by mixing 56.0 mg of methylammonium bromide (MABr, GreatCell Solar) and 183.5 mg of lead(II) bromide (PbBr2, TCI). Salts are dissolved in 1 mL of a 3:1 DMF/DMSO solvent mixture. The resulting solution with a molarity of 0.5 M is stirred for 1 day at 27 °C. Before a film synthesis, glass substrates (12.5 X 12.5 mm) are cleaned by sonication in deionized water, acetone, and 2-propanol. In order to achieve high adhesion, the substrates are then cleaned in an oxygen plasma cleaner. The fabrication of a thin perovskite film is performed in a nitrogen drybox using the spin-coating method. Thirty ftL of perovskite solution is deposited on the substrate and spun at 3000 rpm for 40 s. At the 25th second, 300 ftL of toluene is dripped on the top of the rotating substrate. After spinning, the MAPbBr3 film in the intermediate phase without thermal annealing is taken from the glovebox for further structuring using a nanoimprint lithography method.39

As a mold for the nanoimprint, we use a one-dimensional periodic grating with a period of 750 nm, ridges height of 100

nm, and ridge width of 520 nm. The mold is cleaned in methanol and deionized water and then dried before the imprint. The imprint process is carried out under 4 MPa pressure for 10 min, then the mold is removed. Finally, the imprinted perovskite sample is annealed at 70 °C for 10 min. After the nanoimprint process, the perovskite nanograting is formed with the profile inverted with respect to the one of the mold employed.

Optical Measurements. In order to experimentally confirm the realization of the strong coupling regime in our sample at different temperatures, we use the angle-resolved spectroscopy methods. For this purpose, the back focal plane (BFP) of the objective lens Mitutoyo NIR X50 with NA equal to 0.65 is imaged to a slit spectrometer coupled to the liquid-nitrogen-cooled imaging CCD camera (Princeton Instruments SP2500+PyLoN). A halogen lamp is employed for the white light illumination in angle-resolved reflectance measurements. The white light homogeneously fills BFP, ensuring light incidence at the sample from the whole available range of angles. The reflected light passes through a linear polarizer with an electric field parallel to the grating ridges such that only TE modes are analyzed. Light is then dispersed by a monochromator and detected by the imaging CCD camera. As a result, we obtain the angular dependence of the reflectance spectra. The map shown in Figure 1e is obtained at room temperature and correlates well with the simulated one presented in Figure 1f, which confirms the sufficient accuracy of the structural and optical parameters used in the simulation.

ACS Photonics

pubs.acs.org/journal/apchd5

In both Figures 1e,f one can observe the curvature of the optical mode dispersion in the vicinity of the exciton resonance around 2.31 eV, which is a clear signature of strong exciton— photon coupling and polaritonic behavior. Due to the high absorption in the range of photon energies above the exciton level, upper polariton branch is completely suppressed and cannot be observed in the experiment [see Figure S2 in Supporting Information (SI) for details].

To study the light—matter coupling in our sample we perform angle-resolved photoluminescence (PL) measurements using the setup described above. To excite the sample nonresonantly, we use the femtosecond (fs) laser (Pharos, Light Conversion) coupled with the broad-bandwidth optical parametric amplifier (Orpheus-F, Light Conversion) at a wavelength of 490 nm (2.53 eV), 220 fs pulse duration, and 100 kHz repetition rate. The sample is mounted in the ultralow-vibration closed-cycle helium cryostat (Advanced Research Systems) and is maintained at a controllable temperature in the range of 7—300 K.

■ RESULTS

Temperature-Dependent Strong Light—Matter Coupling. In order to characterize the structural properties of the resulting perovskite PCS, we use atomic force microscopy (AFM) and scanning electron microscopy (SEM) methods, Figure 1b—d. The obtained data confirm the high quality of the imprinted periodic nanograting and allow the precise determination of its parameters, in particular, the period of the structure of750 nm, ridge height of45 nm, and ridge width of 200 nm (Figure 1c,d). Note that rare pinholes in the sample, shown in Figure 1d, appear after nanoimprint and play a negligible role in the resulting optical quality of the sample. With extracted grating parameters and accounting for the measured refractive index dispersion of MAPbBr3 thin films,40 we calculate the angle-resolved reflectance spectrum (Figure 1f) by the Fourier modal method (FMM).41

Figure 2a shows the measured angle-resolved PL spectra for the temperatures varying from 20 to 295 K. The spectral maps reveal two features: the narrow-band angle-dependent polar-iton mode and a PCS-uncoupled dispersionless emission in the vicinity of the exciton resonance. With an increase in the temperature, we clearly observe the pronounced blueshift of both the uncoupled PL peak and the polariton mode.

In order to carefully analyze the evolution of exciton-polaritons with an increase of the temperature, we fit the polariton dispersion using two-coupled oscillator model:43

ELP(K) =

Ex + 2Ec(K) - ^(Ex-Tc(kx)f + 4g0

(1)

where Ex = Ex — iyx is a complex exciton energy and Ec(kx) = Ec(kx) — iyc(kx) is a complex photonic cavity mode energy, with imaginary parts Jx and Jc being the characteristic broadenings of excitonic and photonic modes, respectively, and kx is the in-plane component of the wavevector of light. Within the light cone, the excitonic dispersion can be safely neglected. g0 is the strength of the light—matter coupling, which together with the broadenings of the modes define the Rabi splitting as follows:

The excitonic and photonic fractions in a lower polariton (I XkI2 and ICkl2, respectively), known as Hopfield coefficients, are shown in Figure 2b. They depend on a wavevector and can be extracted using the fitting parameters of the dispersions using the following relations:

X I2 = -

Ec(k)- Ex

J(Ec(k)- Ex)2 + <

^ = №- (C~ ïx?

(2)

(3)

The uncoupled cavity mode (orange lines in Figure 2a) is obtained by a linear extrapolation of the leaky mode dispersion from the spectral region far from the excitonic resonance to the whole spectral range. The polariton dispersion Re( ELP(k)) is extracted from the measured angle-resolved PL spectrum by fitting the mode resonance at each in-plane wavevector kx/k0 by the Lorentz peak function. Here, k0 is the wavevector of light in free space defined as k0 = E/(h-c), where E is the photon energy and c is the speed of light. Note that in recent works some uncertainty in the determination of exciton resonance in MAPbBr3 with various methods was re-ported,33,35 and we therefore choose Ex and g0 in eq 1 as optimization parameters for each temperature in our fitting procedure.

Figure 2d shows the temperature dependence of the coupling coefficient g0. The fitting procedure also allows to extract the values of Yc ~ 20 meV and yx < jXT ^ 12 meV, where is the room temperature exciton line width [see SI]. Taking into account the strong light-matter coupling criteria g0 > Iyc — YxI/2 and > (yc + Yx)/2, we confirm that in our system exciton-polaritons remain stable up to the room temperatures. In particular, at room temperature, we get the value g0 = 54 ± 0.5 meV, which exceeds the value of g0 = 48 meV reported previously for the geometry with a vertical Bragg cavity. The error is estimated as the standard deviation of the optimized parameter in fitting. This enhancement can be attributed to a better field localization in our PCS sample.

The temperature dependence of the position of the excitonic resonance (Figure 2c) extracted from the two-coupled oscillator model is in good agreement with previous works.33,35 Note that in the case of fitting an uncoupled resonance from the reflectance measurements,33 one should account for the inhomogeneous broadening of the excitonic line, while in the case of the strong exciton—photon coupling, this broadening is lifted due to the effect of motional narrowing.44 The pronounced temperature dependence of the position of the excitonic level is the signature of strong polaronic effects in the linear optical response.33 Below we demonstrate that these effects play a crucial role in the nonlinear optical response in MAPbB^ as well.

Nonlinear Polariton Blueshift under Resonant Pump. In order to study the role of the polaronic effects in polariton nonlinearity, we first perform resonant pump-dependent reflectivity measurements. The sample is excited by 220 fs pulses with tunable central wavelength. The angle of the incidence is controlled by the focusing of the laser beam to the back focal plane of an objective lens. We select several angles of pump incidence for near-resonant excitation of polaritons with different excitonic fractions defined by the Hopfield coefficient IXkl2, eq 3. We measure the reflectance spectra within the spectral range of the pump fs laser and extract the polariton resonance peak parameters by fitting it with a Fano line shape function. With increase of the pump fluence, we

Article

; IC.I2 = 1 - IX, I2

1 -

ACS Photonics

pubs.acs.org/journal/apchd5

observe the nonlinear blueshift of the lower polariton branch. The measured blueshifts as functions of the incident fluence for different wavevectors (corresponding to different values of Hopfield coefficients) are shown in Figure 3a with circles of

0 200 400

Fluence, uJ/cm:

0 5000 10000

Fluence, uJ/cm2

Figure 3. (a) Extracted polariton blueshift as a function of incident pump fluence of the femtosecond laser excitation at room temperature. The thin solid lines are the results of theoretical modeling. Inset table shows coefficients IXfcl2 for excitonic fractions in polaritons. In the experiment, the observable blueshifts are limited by the spectral line width of the pulse. We therefore perform the numerical simulations for the same set of parameters within the extended range of pump fluences reaching the blueshift saturation, as shown in panel (b). Inset: Wavevector dependence of polariton nonlinearity rates associated with exciton—exciton Coulomb interaction (blue curve) and the quench of Rabi splitting due to the phase space filling (green curve). The vertical dashed lines of corresponding color indicate the experimental wavevectors shown in panels (a) and (b). The nonlinearity associated with the quench of Rabi splitting is comparable with exciton—exciton interactions, which stems from the very large value of bare light—matter coupling go = 54 meV.

the different colors. Higher polariton blueshifts are observed for higher excitonic fractions . For the highest excitonic fraction, we achieve the maximum measured blueshift of 6.4 meV. The experimental value of the polariton blueshift is limited by the spectral line width of the resonant pump, discussed in detail below, and can be expected to increase even further.

We now proceed with the theoretical model for the quantitative description of the polaron-assisted polariton nonlinearity, which will allow us to describe the presented experimental data. The Schrödinger equation for an excitonic state in the center of mass coordinates reads:

2

-V (1 )

V(1 ) = ~Eb¥(r)

(4)

where pi * = m*m*/(m* + m*) is the exciton reduced mass, with m* and m* being the masses of electrons and holes. In halide perovskites, the strong coupling between the charge carriers and longitudinal optical (LO) phonon modes leads the formation of polarons and corresponding renormalization of the charge carrier effective masses, which can be represented

34

me[h] • where

e[h] -

= me[h](1 + <W6)

we[h]

ZET.n

(5)

(6)

is the dimensionless Frohlich coupling constant. In the above expression Elo is the energy of LO phonon, e is the elementary charge, £0 is the vacuum permittivity, and

1

1

1

e £oo £s (7)

with £s and being static and high frequency dielectric constants, respectively.

Besides effective mass renormalization, polaronic effects strongly affect the interaction between the charge carriers, which within the Bajaj approach can be represented as45,46

V (r) = — 1 + M (e^ + e-"1*)

Алел

le *

(8)

where y = 0.14 is the optimization parameter, and 1e[h] = &/^2ELOme[h] are the polaron radii.

For numerical calculations, we use parameters from refs 33 and 46. We set = 4.4, £s = 25.5, Elo = 16.7 meV, me = 0.21 m0, and mh = 0.25m0, where m0 is the free electron mass. We numerically calculate the eigenvalues of eq 4 and obtain the excitonic binding energy Eb = 30.5 meV, which is in line with previous reports.33,35 We mention that the large binding energy stems solely from polaronic effects. In the absence of polaronic effects, the severe dielectric screening of the Coulomb interaction would result in a binding energy of order of 2—3 meV, being thus unstable at room temperature. The obtained wave function of the ground state of an exciton corresponds to the hydrogen-type expression iff = jL= e r/aB,

where % ~ 1.92 nm is the excitonic Bohr radius.

The high value of the binding energy makes excitons stable at room temperatures. Note that the polaronic renormalization of the effective masses and the interaction potential leads to the violation of conventional hydrogenic Rydberg scaling of exciton energy levels and Bohr radius.47 It also modifies substantially the relations between the exciton Bohr radius (which defines the maximally reachable exciton density, corresponding to the Mott transition) and the nonlinear interaction rates in a way favorable for enhancing the fluence-dependent blueshift.34

To demonstrate that, we calculated the matrix elements of the exciton—exciton interaction, and Pauli factors responsible for the quenching of the Rabi splitting which governs the nonlinear optical response. The resulting blueshift of the lower polariton mode can be represented in the form of a series of terms for the polariton density nLk.48,49 Keeping only the terms linear and quadratic in nLk one gets

, nLk)* U(kx)nLk- U2(hx)n2Lk + O(nLk) (9)

where the expansion coefficients read34,49

U(kx) « 1X214 + «os K/iXtC + XtCk) = Uxx(kJ + ujkj

(10)

U2(h)* IVXX2\\Xl\6 + g0ls2IIXll4(X*Cl + XtC*) = UXX2(kx) + U^iK)

(11)

Each of the terms represents the sum of the contributions stemming from the exciton—exciton scattering and renormal-ization of the Rabi splitting, the latter being governed by the saturation rates s and S2. The explicit expressions and the details of calculation for the corresponding parameters are

Article

rv2

z

1

e

4тс0 ne

ACS Photonics

pubs.acs.org/journal/apchd5

given in SI. Due to the hydrogen-type shape of the excitonic wave function, the saturation factors can be computed analytically, as 5 = 7ira|, s2 = — 253;r2aB/4. The calculated values of the exciton-exciton Coulomb scattering matrix elements are Vxx = 0.022 feV^m3, Vxx2 = -1.51 X 10-9 feV^fm6. The Coulomb nonlinearity rates were calculated accounting for the polaronic effects, which effectively enhance the maximally possible blueshift, as compared to conventional bulk hydrogen-like excitons.34

In order to determine the dependence of the polariton density on the intensity of a resonant pump in nonlinear experiments, we use the input-output formalism. In the mean field approximation, the polariton density can be written as the square of the absolute value of the lower polariton field, nLk = Ip I2, where p = (PLk), with pLk being the lower polariton annihilation operator.

The dynamic equation for p reads

npt = -iE^^- rLKl + fk- xivfa - mijpfpk

+ 3iU2(kx) \p\% +

-t2/(2ip) -im.t -a0e pe L

(12)

where YL(kx) [y'] are radiative [nonradiative] decay rates of the lower polariton branch, Tp is the pulse duration, Wl is the pump frequency, and a0 is the square root of the number of photons passing through the structure per unit time per unit area, which is related to the peak incident power density as a0 = ^, with F being the pump fluence and Lc = 0.3 ffm the thickness of the sample. We found the ratio Yl(^x)/ [YL(kx) + Y ] ~ 0.15 in a wide range of the values of kx. The parameter Y2 is the exciton—exciton annihilation rate, defined by collisional broadening.7 Due to near-resonant character of the pump, we assume only exciton-polaritons with a given wave vector are formed and neglect the possible formation of incoherent exciton reservoir. We numerically simulate eq 12 and assume that the optical response is collected at maximal density, nLk = nLk(^)lmax. The exciton—exciton annihilation rate is treated as fitting parameter and chosen as Y2 = 2Vxx.

The developed theory allowed us to fit the experimental values of the blueshift as functions of the fluence. The contributions of both exciton—exciton interaction and absorption saturation were accounted for and are both determined by excitonic fraction in a lower polariton, which varies with the in-plane wave vector kx. This fact explains the wave-vector dependence of the nonlinear blueshift, shown in Figure 3.

The trend toward the saturation of the blueshift with increase of the fluence, clearly visible in Figure 3b, can stem from the quadratic in density terms, which have the sign opposite to the linear terms and thus describe the redshift contribution (see eqs 9 and 11). However, our estimation showed that in such mechanism the blueshift saturation effects should become visible only for the fluences F > 1000 fJ/cm2.

We therefore attribute the sublinear fluence dependence of polariton blueshift in our case shown in Figure 3a primarily to exciton—exciton annihilation, which limits the increase of the polariton density with pump fluence. It was found earlier and confirmed by our experiments, that MAPbBr3 films can support further increase of fluence up to F ~ 104 fJ/cm2 without irreversible changes in a sample50,51 and allow to reach up to 1019 cm-3 of polariton density.52 In our experiment, the

maximum observable mode blueshift of tt6 meV is limited by the spectral line width of femtosecond laser radiation 14 meV). For larger blueshifts, the overlap between the spectral profile of the polariton mode (with the line width of« 15 meV) and the accessible spectral range defined by the spectrum of the pulse becomes insufficient, which makes the extraction of the blueshifted mode position inaccurate. We therefore theoretically simulate this hypothetical regime and find that one can expect a blueshift as large as 20 meV (see Figure 3b), similar to that observed in ref 34 for MAPM3 at cryogenic temperatures.

The relative impact of the two components of nonlinearity is presented in the inset of Figure 3b. Notably, the contribution stemming from the quench of the Rabi splitting is quite large and comparable with the contribution coming from exciton— exciton scattering. This situation is quite unusual and is due to the large value of light—matter coupling go ~ 50 meV.

■ CONCLUSION

We have demonstrated the robust polariton nonlinear response in MAPbBr3 hybrid perovskites at room temperature. For this purpose, using the nanoimprint lithography, we have fabricated a MAPbBr3-based photonic crystal slab cavity supporting strong exciton—photon coupling in a wide temperature range. By fitting the polariton dispersions, we have revealed the substantial variation of the exciton transition energy with temperature, which is a fingerprint of the polaron effects in the studied system. These effects are responsible for the stability of the excitons at room temperatures and the enhancement of the optical nonlinearity detected as the blueshift of the lower polariton line under resonant femtosecond pump. We have developed the corresponding theoretical model and have demonstrated that the contribution associated with the phase space filling effects can be comparable and even exceed the one provided by exciton—exciton scattering. Predicted values of the blueshift achievable in MAPbBr3 at room temperature exceed 20 meV, which enables good means for the realization of high-contrast optically induced polaritonic potentials for the study of the interacting polariton fluids and their applications in optical analog simulators.

■ ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphotonics.2c01773.