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北海道大學工學部研究報告 = Bulletin of the Faculty of Engineering, Hokkaido University

Phase Diagram Approach to the Polaron Problem

Akihiro Hashimoto, Naoki Tokuda

Published Mar 25, 1986• 0 citations
OpenAlex

Abstract

The problem of an electron interacting wlth acouseic as well as with optical modes of lattice vibrations is investlgated wlthin the modjfjed variatioRal scheme of the Lee-Low -Pines theory. lt is shown that the po}aron changes its state according to the values of the electroR-optical phonon and £he electron-acoustic phonoR coupling constants by examining the ground-state energy, the mean numbers of the optical and acoustic phonons iR the cloud around the e}ectron and the spatlal localization of the electron as fuRctions of the coupling

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The problem of an electron interacting wlth acouseic as well as with optical modes of lattice vibrations is investlgated wlthin the modjfjed variatioRal scheme of the Lee-Low -Pines theory. lt is shown that the po}aron changes its state according to the values of the electroR-optical phonon and £he electron-acoustic phonoR coupling constants by examining the ground-state energy, the mean numbers of the optical and acoustic phonons iR the cloud around the e}ectron and the spatlal localization of the electron as fuRctions of the coupling
The optical polaron bounded in a Coulomb potential is investigated within the modified variational scheme of the Lee-Low-Pines theory (1953) which is valid for the whole range of the electron-phonon coupling. The ground state energy, the mean number of phonons in the cloud around the electron and the spatial localisation of the electron for the optical polaron change abruptly at certain values of the electron-phonon coupling constant alpha and of the Coulomb potential beta . The polaron changes its state according to the values of the parameters alpha and beta . Such features are summarised in the phase diagram.
The polaron features for long-range electron–phonon interaction are investigated by extending a variational approach previously proposed for the study of systems with local coupling. The ground state spectral weight, the average kinetic energy, the mean number of phonons, and the electron–lattice correlation function are discussed for a wide range of model parameters focusing on the adiabatic regime and comparing the results with the short-range case (Holstein model). A strong mixing of electronic and phononic degrees of freedom for small values of the electron–phonon coupling constant is found in the adiabatic case due to the long-range interaction. Finally a polaron ‘phase diagram’ is proposed.
The polaron problem is treated in a self-consistent manner. The treatment is based on Heisenberg's equations of motion starting from a trial expression for the electron position which includes only one real phonon but any number of virtual phonons. Numerical results for the polaron effective mass and the optical-absorption coefficient are given for electron-LO-phonon coupling strengths ranging from 0 to 4.5. The results are discussed and compared with those obtained by Feynman and by Lee, Low, and Pines.