The polaron-like nature of an electron coupled to phonons

TL;DR

This paper reviews how electrons coupled with phonons can behave as free particles or form polarons with increased mass, analyzing the Holstein model across dimensions and noting the low coupling strength for crossover.

Contribution

It provides a comprehensive summary of polaron formation in the Holstein model across different dimensions and identifies the coupling strength at which crossover occurs.

Findings

Polaron formation occurs at relatively low coupling strengths.

Crossover behavior varies with dimensionality.

The Holstein model effectively captures polaron physics.

Abstract

When an electron interacts with phonons, the electron can exhibit either free electron-like or polaron-like properties. The latter tends to occur for very strong coupling, and results in a phonon cloud accompanying the electron as it moves, thus raising its mass considerably. We summarize this behaviour for the Holstein model in one, two and three dimensions, and note that the crossover occurs for fairly low coupling strengths compared to those attributed to real materials exhibiting conventional superconductivity.