Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap

Anna Miglio,Steven G Louie,Gabriel Antonius,Xavier Gonze,Emile Godbout,Michel Côté,Matteo Giantomassi,Yang-Hao Chan,Véronique Brousseau-Couture

doi:10.1038/s41524-020-00434-z

Abstract

Electronic and optical properties of materials are affected by atomic motion through the electron–phonon interaction: not only band gaps change with temperature, but even at absolute zero temperature, zero-point motion causes band-gap renormalization. We present a large-scale first-principles evaluation of the zero-point renormalization of band edges beyond the adiabatic approximation. For materials with light elements, the band gap renormalization is often larger than 0.3 eV, and up to 0.7 eV. This effect cannot be ignored if accurate band gaps are sought. For infrared-active materials, global agreement with available experimental data is obtained only when non-adiabatic effects are taken into account. They even dominate zero-point renormalization for many materials, as shown by a generalized Fröhlich model that includes multiple phonon branches, anisotropic and degenerate electronic extrema, whose range of validity is established by comparison with first-principles results.

Highlights

The electronic band gap is arguably the most important characteristic of semiconductors and insulators
The vast majority of first-principles calculations relies on Kohn–Sham Density-Functional Theory (KSDFT), valid for ground state properties[2], that delivers a theoretically unjustified value of the band gap in the standard approach, even with exact KS potential[3,4,5]
Comparing with experimental band gaps, we show that adding zero-point renormalization of the gap (ZPRg) improves the GWeh first-principles band gap, and that the ZPRg has the same order of magnitude as the G0W0 to GWeh correction for half of the materials on which GWeh has been tested

Summary

Introduction

The electronic band gap is arguably the most important characteristic of semiconductors and insulators. The breakthrough came from many-body perturbation theory, with the so-called GW approximation, first non-self-consistent (G0W0) by Hybertsen and Louie in 19866, twenty years later self-consistent (GW)[7] and further improved by accurate vertex corrections from electron-hole excitations (GWeh)[8]. The latter methodology, at the forefront for band-gap computations, delivers a 2–10% accuracy, usually overestimating the experimental band gap. GWeh calculations are computationally very demanding, typically about two orders of magnitude more than

Methods

Results

Conclusion