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Journal of Physics C Solid State Physics

The one-dimensional acoustic polaron via the deformation potential under the influence of a Coulombic impurity and its phase diagram

Naoaki Tokuda, Hatsuhiro Kato

Published Jul 20, 1982• 7 citations
Publisher

Abstract

The one-dimensional acoustic polaron via the deformation potential under the influence of a Coulombic impurity is investigated within the modified variational scheme of the Lee-Low-Pines theory which is valid for the whole range of the electron-phonon coupling. The phase diagram obtained shows how the one-dimensional polaron changes its state according to the values of the electron-phonon coupling constant and of the Coulombic impurity potential.

DOI
10.1088/0022-3719/15/20/001

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arXiv:1209.5975•Physical Review B•Oct 8, 2012•18 citations
The one-dimensional acoustic polaron via the deformation potential under the influence of a Coulombic impurity is investigated within the modified variational scheme of the Lee-Low-Pines theory which is valid for the whole range of the electron-phonon coupling. The phase diagram obtained shows how the one-dimensional polaron changes its state according to the values of the electron-phonon coupling constant and of the Coulombic impurity potential.
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.
We have studied one dimensional acoustic phonon linearly coupled to the electron density. The phonon spectrum is linear with cutoff at the Debye frequency, it is straightforward modification of three dimensional optical phonons. Phonon field results in substituting the dynamical coupling for the screened coulomb interaction. We have shown that the electron-phonon coupling quantitatively changed the phase diagram of Luttinger liquid with a single impurity. The existence of slow and fast polaron modes with different weights in different regimes resulted in different renormalization group flow for a weak scatterer and a weak tunneling link. The resulting phase diagram depending on the parameters of the problem, regimes corresponding to purely metallic or purely insulating behavior and an intermediate regime with two stable fixed points and one unstable, finite conductance fixed point. we have found that the direction of renormalization group flow change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. The obtained results were found in good agreement with previously obtained results.
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
We calculate the low-temperature properties of an acoustic polaron in three dimensions in thermal equilibrium at a given temperature using a specialized path-integral Monte Carlo method. In particular we find numerical evidence that the chosen Hamiltonian for the acoustic polaron describes a phase transition from a localized state to an unlocalized state for the electron as the phonon-electron coupling constant decreases. The phase transition manifests itself with a jump discontinuity in the potential energy as a function of the coupling constant. In the weak coupling regime the electron is in an extended state whereas in the strong coupling regime it is found in a self-trapped state.