High-throughput analysis of Fr\"ohlich-type polaron models

TL;DR

This study performs a high-throughput analysis of Fr"ohlich-type polaron models across over a thousand materials, identifying their applicability limits and exploring the behavior of polarons in various electronic structures.

Contribution

The paper introduces a comprehensive analysis comparing standard and generalized Fr"ohlich models, revealing their limits and the conditions under which they accurately describe polaron behavior.

Findings

Most materials exhibit large polaron behavior and validate perturbative treatment.

A significant fraction of materials show breakdown of perturbative treatment or small self-trapping regions.

Ab initio calculations reveal cases with large zero-point renormalization energies.

Abstract

The electronic structure of condensed matter can be significantly affected by the electron-phonon interaction, leading to important phenomena such as electrical resistance, superconductivity or the formation of polarons. This interaction is often neglected in band structure calculations but can have a strong impact on band gaps or optical spectra. Commonly used frameworks for electron-phonon energy corrections are the Allen-Heine-Cardona theory and the Fr\"ohlich model. While the latter shows qualitative agreement with experiment for many polar materials, its simplicity should bring hard limits to its applicability in real materials. Improvements can be made by introducing a generalized version of the model, which considers anisotropic and degenerate electronic bands, and multiple phonon branches. In this work, we search for trends and outliers on over a thousand materials in existing databases of phonon and electron band structures. We use our results to identify the limits of applicability of the standard Fr\"olich model by comparing to the generalized version, and by testing its basic hypothesis of a large radius for the polaronic wavefunction and the corresponding atomic displacement cloud. Among our extended set of materials, most exhibit large polaron behavior as well as validity of the perturbative treatment. For the valence band, there is also a significant fraction of the materials for which the perturbative treatment cannot be applied and/or for which the size of the self-trapping region is close to the atomic repetition distance. We find a large variety of behaviors, and employ much more accurate, fully ab initio Allen-Heine-Cardona calculations to understand extreme cases, where the Fr\"ohlich model should fail and unusually large zero-point renormalization energies occur.