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Journal of Physics C Solid State Physics

The optical polaron bound in a Coulomb potential and its phase diagram

Naoaki Tokuda, H Shoji, K Yoneya

Published Oct 20, 1981• 19 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3719/14/29/015

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Journal of Physics C Solid State Physics•Mar 30, 1981•40 citations
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 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
Based on the unitary transformation, a general treatment of the bound polaron is proposed. In distinction from earlier calculations, the present method gives explicit expressions for not only the energy but also the wave functions both in the ground state and in the excited states such as the relaxed excited state and the phonon scattering state. These expressions involve a summation on the complete set of eigenstates of a trial Hamiltonian, and in actual calculations the Coulomb Hamiltonian and the harmonic oscillator Hamiltonian are chosen as trial Hamiltonians. For the ground state, the energy expression is the same as that obtained by Matsuura with the path integral method. The present method is valid in the whole region of the electron-phonon coupling constant α and Coulomb force β except for β→0 and α>6.