Unified approach to polarons and phonon-induced band structure renormalization

TL;DR

This paper introduces a unified many-body Green's function approach to accurately model phonon-induced band structure changes, capturing both weak and strong electron-phonon coupling regimes, including polaron formation.

Contribution

It develops a self-consistent Green's function theory that seamlessly integrates perturbative and polaronic effects, extending beyond traditional Allen-Heine methods.

Findings

Reproduces path-integral and Monte Carlo results across all couplings.

Accurately calculates zero-point band gap renormalization with polaron effects.

Unifies descriptions of weak and strong electron-phonon interactions.

Abstract

Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green's function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fr\"ohlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.