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Journal of Physics C Solid State Physics

Analytical investigation of the polaron problem

И. Д. Феранчук, S I Fisher, L I Komarov

Published Sep 20, 1985• 11 citations
Publisher

Abstract

Analytical approximations for the ground state energy of the polaron and for its effective mass are obtained throughout the entire range of the electron-phonon interaction constant. The detailed structure of the phase transition in the polaron system is considered on the basis of these results. Numerical calculations corroborate the analytical conclusions.

DOI
10.1088/0022-3719/18/26/019

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The Ground State of the Optical Polaron in the Strong-Coupling Case

Satoru J. Miyake

The next lowest order term of the ground state energy has its origin in lowering of frequencies of phonons localized around the polaron. An eigenvalue equation is derived, the solution of which gives phonon eigenmodes and frequencies in the presence of the polaron. Several eigenvalues are obtained by numerical integration. From the results, the ground state energy is estimated as \(E_{0}/\hbar\omega_{0}{=}-0.108513\alpha^{2}-2.836+O(1/\alpha^{2})\), where ω 0 is the frequency of the optical phonon and α is the electron-phonon coupling constant. The numerical value of the effective mass is 0.0227019α 4 .

Journal of the Physical Society of Japan•Sep 15, 1976•69 citations
Analytical approximations for the ground state energy of the polaron and for its effective mass are obtained throughout the entire range of the electron-phonon interaction constant. The detailed structure of the phase transition in the polaron system is considered on the basis of these results. Numerical calculations corroborate the analytical conclusions.
A concise approach for static polarons is extended to study the dynamic polaron system having nonspherical symmetry. The general properties of moving polarons, such as the ground-state energy, the phonon number, the effective mass, and the density distribution of phonon momentum---studied as functions of the total polaron momentum and electron-phonon coupling strength---are calculated numerically in a wide range of intermediate coupling strengths. In particular, a modified Fr\"ohlich Hamiltonian is derived for the problem of polaron momentum Q\ensuremath{\geqslant}1. \textcopyright{} 1996 The American Physical Society.
The next lowest order term of the ground state energy has its origin in lowering of frequencies of phonons localized around the polaron. An eigenvalue equation is derived, the solution of which gives phonon eigenmodes and frequencies in the presence of the polaron. Several eigenvalues are obtained by numerical integration. From the results, the ground state energy is estimated as E0/ℏω0=−0.108513α2−2.836+O(1/α2)E_{0}/\hbar\omega_{0}{=}-0.108513\alpha^{2}-2.836+O(1/\alpha^{2})E0​/ℏω0​=−0.108513α2−2.836+O(1/α2), where ω 0 is the frequency of the optical phonon and α is the electron-phonon coupling constant. The numerical value of the effective mass is 0.0227019α 4 .