Perturbation theory of the mass enhancement for a polaron coupled to acoustic phonons

TL;DR

This paper investigates how an electron's effective mass is increased due to coupling with acoustic phonons across different dimensions, using perturbative methods to analyze spectral properties and polaronic behavior.

Contribution

It introduces a perturbative approach to analyze mass enhancement for a polaron coupled to acoustic phonons in various dimensions, comparing results with other models.

Findings

Polaronic behavior is always present in one dimension.

Unusual relation between effective mass and quasiparticle residue in 1D.

Spectral function and quasiparticle residue depend on phonon frequency.

Abstract

We use both a perturbative Green's function analysis and standard perturbative quantum mechanics to calculate the decrease in energy and the effective mass for an electron interacting with acoustic phonons. The interaction is between the difference in lattice displacements for neighbouring ions, and the hopping amplitude for an electron between those two sites. The calculations are performed in one, two, and three dimensions, and comparisons are made with results from other electron-phonon models. We also compute the spectral function and quasiparticle residue, as a function of characteristic phonon frequency. There are strong indications that this model is always polaronic on one dimension, where an unusual relation between the effective mass and the quasiparticle residue is also found.