2024-07-17T19:41:35Z
https://ir.soken.ac.jp/oai
oai:ir.soken.ac.jp:00000664
2023-06-20T14:51:11Z
2:428:15
Path-Integral Theory for Photoemission Specta of Electron-Phonon Coupled Systems
Path-Integral Theory for Photoemission Specta of Electron-Phonon Coupled Systems
吉, 凱
ジ, カイ
JI, Kai
It has been a long-standing question in solid state physics, how the electron-phonon (e-ph) interaction influences the electronic energy band structures, and finally determines a material to become an insulator, metal or superconductor. Since the photoemission spectrum can directly probe this structure of electronic energy bands and topology of Fermi surface, it has become one of the most important measurements for the experimental studies. In the angle resolved photoemission spectra (ARPES) , the binding energy can now be measured as a function of each given momentum. With the rapid progress of this high resolution ARPES, the electronic energy band structure can now be discerned in the scale of a few meV. Based on this technical development, quite a lot of new properties associated with e-ph interaction have been discovered in the normal metallic states as well as in the superconducting (SC) ones, signifying direct and clear evidences for the importance of the e-ph interactions. On the other hand, theoretical studies for this e-ph coupling already have a long history. In the case of a single electron coupled with phonons, it has been investigated in detail, by the ordinary perturbation theory, and also by the unitary transformation methods. As for the many-electron system coupled with phonons, the so-called Migdal-Eliashberg (ME) theory, and also adiabatic or mean field approximation are often used to clarify the energy band structures, in connection with various phase transition phenomena, such as the charge density wave (CDW) states and superconductor ones from metallic states. In some cases, systematic theoretical methods have already been devised to take into account high order corrections, which are not included in the ordinary perturbation theories. However, these existing theories seem to be not so useful to clarify the aforementioned ARPES, since it spans the whole momentum region from the Fermi level (≡E<SUB>F</SUB> ) to the bottom of the valence band. According to recent experimental results, it has become clear that the ARPES evolve quite drastically as the momentum changes from E<SUB>F</SUB> to the band bottom. This spectral evolution appears quite universal for a wide varieties of e-ph systems, especially the intermediately coupled metallic ones. However, its origin seems beyond the conventional approximation theories mentioned above. Thus, the problem how e-ph interaction dominates the spectral shape has now emerged as a new challenge for the theory of solid state physics. <br /> In this work, we present a new path-integral theory to calculate the ARPES of e=ph coupled systems. Our main purpose of this paper is to clarify the impact of e-ph interaction on the lineshape of ARPES. we consider a many-electron system coupled with Einstein phonons, which is often called Holstein model. This model has been studied extensivery, with various interests ranging from the competition between metallic, CDW and SC phases, to the energy gap opening, by perturbative and non-perturbative methods. In our numerical calculation, the path-integral is performed by the quantum Monte Carlo (QMC) simulation. Thus it is completely free from any other approximations. Give the QMC data of imaginary time Green's function, we reproduce the spectral function by the analytic continuation. By this means, we systematically study the spectral properties of the e-ph coupled systems based on the one-dimensional and two-dimensional (2D) Holstein models under various conditions. We find the band structure is greatly modified by the multiple scattering effect of electron with phonons, even if the whole system is still metallic and the e-ph coupling strength is intermediate. Around the band bottom, the spectrum takes a broad Gaussian, indicating the electron in this state is nearly localized and incoherent. While near the E<SUB>F</SUB>, the spectral shape is characterized by an asymmetric two-headed Lorentzian, which means the electron in this state is almost coherent with a plane wave nature, extending over all the crystal. There are also dimensionality effects on the phonon peaks, which make them most clearly observed in the 2D non-half-filled cases with no CDW gap. Our results qualitatively agree with recent experiments of high resolution ARPES on Be (0001) surface and Bi<SUB>2</SUB>Sr<SUB>2</SUB>CaCu<SUB>2</SUB>O<SUB>8</SUB>.
総研大甲第744号
eng
thesis
https://ir.soken.ac.jp/records/664
博士（理学）
2004-03-24
総合研究大学院大学
https://ir.soken.ac.jp/record/664/files/甲744_要旨.pdf
application/pdf
284.6 kB
2016-02-17