Trapping of three-dimensional Holstein polarons by various impurities

TL;DR

This paper investigates how impurities affect three-dimensional Holstein polarons, revealing that electron-phonon interactions significantly modify impurity potentials and exhibit retardation effects, with results validated against Monte Carlo simulations.

Contribution

It introduces a detailed analysis of impurity effects on Holstein polarons using the momentum average approximation, highlighting the importance of retardation effects ignored by simpler models.

Findings

Electron-phonon coupling causes strong renormalization of impurity potentials.

Retardation effects are significant in the effective impurity potential.

Comparison with Monte Carlo confirms the approximation's accuracy.

Abstract

We study the bound states of a three-dimensional Holstein polaron near various kinds of single impurities, using the momentum average approximation. We show that the electron-phonon coupling is responsible for a strong renormalization of the impurity potential, resulting in an effective potential with significant retardation effects, which describes essential physics ignored by "instantaneous" approximations. The accuracy of our approximation is gauged by comparison with results from Diagrammatic Monte Carlo for the case of an impurity that modifies the on-site energy of the electron. We also discuss impurities that modify the local strength of the electron-phonon coupling, as well as isotope substitutions that change both the electron-phonon coupling and the phonon frequency, and contrast and highlight the difference between these cases.