Effect of electron-phonon interaction on the impurity binding energy in a quantum wire

TL;DR

This study investigates how electron-phonon interactions influence impurity binding energies in cylindrical quantum wires, revealing that polaron effects become more significant as wire radius decreases, with bulk optical phonons being dominant.

Contribution

It introduces a perturbative-variational approach to analyze electron-phonon effects on impurity binding energies in quantum wires, emphasizing the role of bulk and surface optical phonons.

Findings

Polaron effects increase rapidly as wire radius shrinks.

Bulk optical phonons have a dominant role in polaron effects.

Impurity binding energies are significantly affected by electron-phonon interactions.

Abstract

The effect of electron-optical phonon interaction on the hydrogenic impurity binding energy in a cylindrical quantum wire is studied. By using Landau and Pekar variational method, the hamiltonian is separated into two parts which contain phonon variable and electron variable respectively. A perturbative-variational technique is then employed to construct the trial wavefunction for the electron part. The effect of confined electron-optical phonon interaction on the binding energies of the ground state and an excited state are calculated as a function of wire radius. Both the electron-bulk optical phonon and electron-surface optical phonon coupling are considered. It is found that the energy corrections of the polaron effects on the impurity binding energies increase rapidliy as the wire radius is shrunk, and the bulk type optical phonon plays the dominant role for the polaron effects.