Флуктуации заряда и сверхпроводимость в сильно коррелированных электронных системах тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Нгуен Дань Тунг

• Нгуен Дань Тунг
• кандидат наук
• 2023

Оглавление диссертации кандидат наук Нгуен Дань Тунг

Contents

Introduction

1. Relevance of the topic

2. Purpose and objectives of the thesis

3. The main results of the thesis submitted for defense:

4. Scientific novelty

5. Approbation of the thesis

6. Personal contribution of the author

7. Content of the work

Chapter 1 Conductivity in the half-filled ionic Hubbard model

1.1 Model and formalism

1.2 Numerical results and discussion

1.3 Conclusion

Chapter 2 Static and dynamic charge fluctuations in strongly correlated electronic system

2.1 The model and the dynamical charge susceptibility

2.1.1 The t-J-V model

2.1.2 Memory function formalism

2.2 Numerical results and discussion

2.2.1 Static charge susceptibility

2.2.2 Dynamical charge susceptibility

2.2.3 Static charge susceptibility for electron doping

2.3 Conclusion

Chapter 3 Electronic spectrum and superconductivity in the extended t — J — V

model

3.1 General formulation

3.1.1 Extended t — J — V model

3.1.2 Dyson equation

3.2 Generalized mean-field approximation

3.2.1 Normal state

3.2.2 Superconducting state

3.3 Self-energy calculation

3.3.1 Normal state GF

3.3.2 Superconducting state

3.4 Results and Discussion

3.4.1 Model parameters

3.4.2 Normal state

3.4.3 Superconducting state

3.5 Conclusion

Conclusion

Appendix A Calculation of Gao (w)

Appendix B Calculation of mq and

Appendix C Calculation of the spectrum of e(k)

Appendix D Memory function

Appendix E Self-energy

Appendix F Gap equation in the static approximation

Appendix G Numerical calculation

List of Figures

List of Tables

List of abbreviations

Введение диссертации (часть автореферата) на тему «Флуктуации заряда и сверхпроводимость в сильно коррелированных электронных системах»

Introduction

1. Relevance of the topic

Transition metal oxides (TMOs) form probably one of the most interesting classes of solids, exhibiting a wide variety of structures and properties. The unique electrical and magnetic properties of TMOs have attracted the interest of theoretical physicists and technology developers for their applicability. Recently, experiments have provided observable evidence of many exotic phenomena occurring in TMOs, such as charge density waves (CDW) (e.g. K0 3MoO3), charge ordering (e.g. Fe3O4), and defect ordering (e.g. Ca2Mn2O5, Ca2Fe2O5). TMOs can range from ferromagnetic (e.g. CrO2, La05Sr05MnO3) to antiferromagnetic (AFM) (e.g. NiO, LaCrO3). Many oxide compounds have switchable orientation states such as ferroelectric (e.g. BaTiO3, KNbO3) and ferroelastic [e.g. Gd2(MoO4)3]. Some TMOs have metallic properties (e.g. RuO2, ReO3, LaNiO3), while others have highly insulating properties (e.g. BaTiO3). Several oxides exhibit co-existence of metallic and non-metallic properties (e.g. Lu2Rh2O7). Among them, the phenomenon of high-temperature superconductivity (HTSC) in cuprates is one of the issues of interest to solid-state physicists.

The unusual properties of TMOs are clearly due to the unique nature of the outer d or f electrons. The d electrons are localized, their wavefunctions are restricted in a small space around the atom. They are distributed inside a sphere with small radius, this makes the chance of electrons meeting each other higher than other bands, the on-site Coulomb interaction (CI) is thus larger. Therefore, many TMOs belong to strongly correlated materials which have incompletely filled d or f electron shells with narrow energy bands. In these materials, transition metal can easily combine with oxygen to form covalent bond. It gives all s electrons and some d electrons to oxygen, there are only d or f electrons remaining in its outer shell. If TMOs contain the alkaline or rare earth elements, they can provide additional electrons to oxygen. Depending on atomic radius, they can distort the lattice structure. Therefore, the basic electronic structures of TMOs origin from transition metal d bands as frontier bands, oxygen p bands the second most energetic bands staying at the Fermi level, other bands have less significant impact to the electronic properties of these materials.

The theoretical understanding of the properties of various TMO materials is one of major challenges to the modern condensed matter theory. The behavior of electrons and magnetic excitations in these materials cannot be effectively described by traditional one-electron theories, it requires more modern methods to treat these strongly correlated systems which are the reason for the very rich physical properties in TMOs and represented by complicated phase diagrams. Many theories have been proposed to describe corelation electrons in TMOs, among them the dynamical mean field theory (DMFT) is a numerical method that has proved to be very effective. In addition, the Hubbard model is a very useful model for the general description of corelated materials. In the limit of strong correlations, the Hubbard

model can be reduced to the t — J model and with the intersite Coulomb repulsion V, the so called t — J — V model, it turns out to be an effective model for cuprate HTSC. Therefore understanding of physical properties of highly correlated systems and study microscopic models of strong correlations are the actual tasks.

2. Purpose and objectives of the thesis

The goal of the dissertation is the investigation of several properties of TMOs using models of strongly correlated electron systems: the metal-insulator transition (MIT) in the ionic Hubbard model (IHM), static and dynamic charge fluctuations and HTSC within the microscopic t — J — V model. To achieve this goal, the following tasks have been addressed:

1. Obtaining the phase diagram of the half-filled IHM with the on-site Coulomb repulsion U and the

ionic energy A by mean of the coherent potential approximation (CPA). When the system is in the metallic phase a dependence of the dc conductivity on the model parameters is calculated.

2. Calculation of the static charge susceptibility (SCS) and the dynamic charge susceptibility (DCS) in

strongly correlated electronic systems within the two-dimensional t — J — V model. The spectral density and the spectrum of charge excitations as functions of doping and other model parameters are obtained with the use of the equation of motion method for the relaxation functions in terms of the Hubbard operators (HOs).

3. Application of the extended t — J — V model where the intersite Coulomb repulsion and the electron-

phonon interaction (EPI) are taken into account to investigate electronic spectrum and superconductivity in cuprate HTSC. The Dyson equation for the normal and anomalous (pair) Green functions (GFs) is used in the special form where the self-energy is taken in the self-consistent Born approximation (SCBA). Superconducting Tc dependence on EPI and spin-fluctuation interaction is studied.

3. The main results of the thesis submitted for defense:

1. The phase diagram was investigated using CPA in the half-filled ionic Hubbard model (IHM). The

metallic phase was proved to be sandwiched between the band insulator (BI) phase and the Mott insulator (MI) one. The maximum value of the temperature dependent conductivity amax(T) as a function of on-site Coulomb repulsion U occurs near to U « 2A and o~max(T) decreases with increasing T.

2. The behavior of static and dynamic charge susceptibility have been considered in the framework of

the t — J — V model with the Green function (GF) technique. It is shown that with increasing the intersite Coulomb repulsion V, the static charge susceptibility x(q) grows without limit (i.e. 1/x(q) vanishes), and charge density waves arise in the system either along the diagonal of the unit cell or along the edge of the unit cell.

3. Within the t — J — V model, the damping of dynamic charge fluctuations derived from the calculated

imaginary part of the memory function and the GF technique was analyzed for a large range of

doping ¿,0 <6 < 0.3. The behavior was obtained to change from a broad spectrum of overdamped charge fluctuations at 6 « 0.1 to the Fermi-like behavior for 6 > 0.1.

4. The extended t — J — V model with the electron-phonon interaction was applied to study electronic

spectrum and superconductivity for strongly correlated electron system. The Dyson equation for the normal and anomalous GFs was derived in term of Hubbard operators and the self-energy was obtained in the self-consistent Born approximation.

5. Within the approach defined in the point 4 and applied for normal electronic properties, the calculated

GFs revealed a transition from well defined quasiparticle electron excitations to overdamped broad excitations. The sharp Fermi surface in the mean-field approximation in the form of hole pockets at low doping is accompanied by the transformation to arc Fermi surface.

6. The statement on the dominance of the kinematic interaction in the spin fluctuation mechanism of

superconducting pairing, earlier obtained in t — J model, was reexamined in the framework of the extended t — J — V model including electron-phonon coupling ~ g. The statement was confirmed in a wide range of physically significant parameters V and g.

4. Scientific novelty

Several properties of TMOs have been investigated using appropriate models and theoretical methods. The results are in good agreement with experiments. They are the basis of reference for previous controversies and future speculations. Based on these studies, we can understand the phase diagram of the materials, the conditions for the appearance of CDW and the basis for determining the superconducting temperature of corresponding materials. The calculations can be extended to study other properties of TMOs.

5. Approbation of the thesis

The results of the study are published in the following four articles in peer-reviewed journals included in the list:

1. Nguen Dan Tung and Hoang Anh Tuan, Conductivity in the half-filled ionic Hubbard model [Com-

munications in Physics, Vol. 24, No. 3S2 (2014), pp. 34-38].

2. Dan Tung Nguen and N. M. Plakida, Static charge susceptibility in the t — J — V model, [Theoretical

and Mathematical Physics, 2018, 194:1, 127-141].

3. Nguen Dan Tung and N. M. Plakida, Charge dynamics in strongly-correlated electronic systems,

International Journal of Modern Physics B, 32, No. 29 (2018) 1850327 (22 pages).

4. Nguen Dan Tung, A. A. Vladimirov, N. M. Plakida, Electronic spectrum and superconductivity in

the extended t-J-V model, Physica C: 587, 1353900 (1-16) (2021).

The results of the work are presented at international and all-Russian conferences and schools:

1. The XXII International Scientific Conference of Young Scientists and Specialists (AYSS-2018), 23-27 April 2018, JINR, Dubna, Russia.

2. Meeting of the Programme Advisory Committee for Condensed Matter Physics, 14-15 June 2018,

Dubna, Rusia.

3. XXII Scientific School of Young Scientists and Specialists of JINR (LIPNYA 2018), 20-22 July 2018,

Dubna, Russia.

4. The Helmholtz International Summer School «Modern Colliders - Theory and Experiment 2018»,

22 July-1 August 2018, JINR, Dubna, Russia.

5. XXII Training Course in the Physics of Strongly Correlated Systems, 1-12 October, 2018, Vietri sul

Mare (Salerno), Italy.

6. The XXIIIInternational Scientific Conference of Young Scientists and Specialists (AYSS-2019), 15-19

April 2019, JINR, Dubna, Russia.

7. Autumn School on Correlated Electrons: Topology, Entanglement, and Strong Correlations, 21-25

September 2020, Forschungszentrum Jiilich — Online-Edition.

8. The XXIV International Scientific Conference of Young Scientists and Specialists (AYSS-2020), 9-13

November 2020, Dunba, Russia.

6. Personal contribution of the author

The personal contribution of the applicant is to write computational programs, carrying out theoretical calculations, processing the results, as well as analyzing the obtained data and writing articles with supervisor.

Список литературы диссертационного исследования кандидат наук Нгуен Дань Тунг, 2023 год

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