Summary of phycics doctoral thesis: Excitonic condensation in semimetal – semiconductor transition systems

Thesis focus on the problem of “Excitonic condensation in semimetal – semiconductor transition systems” to investigate the nature of the excitonic condensation state in these models by using MF theory. Electronic correlation in the systems is described by the two-band model including electron – phonon interaction and the extended Falicov-Kimball model involving electron – phonon interaction.
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Summary of phycics doctoral thesis: Excitonic condensation in semimetal – semiconductor transition systems MINISTRY OF EDUCATION VIETNAM ACADEMY OF SCIENCE AND TRAINING AND TECHNOLOGY GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY ———————————- DO THI HONG HAI EXCITONIC CONDENSATION IN SEMIMETAL – SEMICONDUCTOR TRANSITION SYSTEMS Major: Theoretical Physics and Maths Physics Code: 9.44.01.03 SUMMARY OF PHYCICS DOCTORAL THESIS Hanoi – 2020 The thesis has been completed at Graduate University of Science and Technology, Vietnam Academy of Science and Technology. Supervisor 1: Assoc.Prof.Dr. Phan Van Nham Supervisor 2: Assoc.Prof.Dr. Tran Minh Tien Reviewer 1: Reviewer 2: Reviewer 3: The thesis will be defended to the thesis committee for the Doctoral Degree, at Graduate University of Science and Technology – Vietnam Academy of Science and Technology, on Date.....Month.....Year 2020. Hardcopy of the thesis can be found at: - Library of Graduate University of Science and Technology - National Library of Vietnam. INTRODUCTION 1. Motivation The condensate state of the electron-hole pairs (or excitons) has recently become one of the attractive research objects. Electrons and holes have semi-integer spin, so the excitons act as bosons and if the temperature is sufficiently low, these excitons can condense in a new macroscopic phase-coherent quantum state called an excitonic insulator – EI. Although first theoretical of the excitonic condensation state in the semimetal (SM) and semiconductor (SC) systems was proposed over a half of century ago but the experimental realization has proven to be quite challenging. In recent years, materials promising to observe EI state have been investigated, such as mixed-valent rare-earth chalcogenide TmSe0.45 Te0.55 , transition-metal dichalcogenide 1T -TiSe2 , semiconductor Ta2 NiSe5 , layer double graphene,... which have increased the studies of the excitonic condensation state both the theoretical side and the experimental side. On the theoretical side, the excitonic condensation state is often studied through investi- gating the extended Falicov-Kimball model by many different methods such as the mean-field (MF) theory and T − matrices, an SO(2)-invariant slave-boson approach, the approximate vari- ational cluster method, projector-based renormalization (PR) method, . . . The authors have shown the existence of the excitonic condensation state near the SM – SC transition. However, in the above studies, investigating the EI state was mainly based on purely electronic charac- teristics with the attractive Coulomb interaction between electrons and holes. Therefore, the coupling of electrons or excitons to the phonon was completely neglected. Besides, when studying the EI state of the semimetallic 1T -TiSe2 by applying BCS su- perconductivity theory to the electron – hole pairs, C. Monney and co-workers have con- firmed that the condensation of excitons affects the lattice through an electron – phonon in- teraction at low temperature. Recently, when studying the condensation state of excitons in transition metal Ta2 NiSe5 by using the band structure calculation and MF analysis for the three-chain Hubbard model phonon degrees of freedom, T. Kaneko has confirmed the origin of the orthorhombic-to-monoclinic phase transition. Without any doubt, lattice distortion or phonon effects are significantly important in this kind of material, particularly, in establishing the excitonic condensation state. Based on this, B. Zenker and co-workers studied the EI state in a two-band model by using the Kadanoff-Baym approach and mean-field Green function, or in the EFK model concluding one valence and three conduction bands by using the MF approximation and the frozen-phonon approximation when considering both the Coulomb in- teraction between the electron – hole and the electron – phonon interaction. The authors have affirmed that that both the Coulomb interaction and the electron – phonon coupling act to- gether in binding the electron – hole pairs and establishing the excitonic condensation state. 1 However, B. Zenker has studied only for the ground state, i.e., at zero temperature. Recently, in Vietnam, investigating EI state in EFK model was also studied by Phan Van Nham and co-workers in a completely quantum viewpoint. By PR method, lattice distortion causing EI state is also intensively studied on the theoretical side, however, only for the ground state. In general, as a kind of superfluidity, the EI state possibly occurs at finite temperature, and at high temperature, it might be deformed by thermal fluctuations. Clearly, the study of the excitonic condensation in Vietnam need to be further promoted. In order to contribute to the development of new research in Vietnam on the excitonic condensation, in the present thesis, we focus on the problem of “Excitonic condensation in semimetal – semiconductor transition systems” to investigate the nature of the excitonic condensation state in these mod- els by using MF theory. Electronic correlation in the systems is described by the two-band model including electron – phonon interaction and the extended Falicov-Kimball model in- volving electron – phonon interaction. Under the influence of Coulomb interaction between electron – hole, the electron – phonon interaction as well as the influence of the temperature or the extenal pressure, the nature of the excitonic condensation state especially the BCS – BEC crossover or competition with the CDW state in the system is clarified. 2. Purpose Investigating the excitonic condensation phase transition in SM – SC transition syst ...