Solution of the Holstein polaron anisotropy problem

TL;DR

This paper investigates how Holstein polarons behave in anisotropic three-dimensional materials, revealing how their properties evolve from one-dimensional to three-dimensional systems and clarifying polaron stability in quasi-one-dimensional substances.

Contribution

The study provides highly accurate variational diagonalization results for polaron mass and radius, elucidating the evolution of polarons with anisotropy and phonon frequency.

Findings

Polaron properties vary smoothly from 1D to 3D with anisotropy.

Holstein interaction enhances charge motion anisotropy.

Polaron stability in quasi-1D systems is clarified.

Abstract

We study Holstein polarons in three-dimensional anisotropic materials. Using a variational exact diagonalization technique we provide highly accurate results for the polaron mass and polaron radius. With these data we discuss the differences between polaron formation in dimension one and three, and at small and large phonon frequency. Varying the anisotropy we demonstrate how a polaron evolves from a one-dimensional to a three-dimensional quasiparticle. We thereby resolve the issue of polaron stability in quasi-one-dimensional substances and clarify to what extent such polarons can be described as one-dimensional objects. We finally show that even the local Holstein interaction leads to an enhancement of anisotropy in charge carrier motion.