Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fr\"ohlich model

TL;DR

This study investigates how spin-orbit coupling influences the zero-point renormalization of electronic band gaps in cubic materials, combining first-principles calculations with an extended Fr"ohlich model to reveal significant effects and modeling subtleties.

Contribution

It introduces a generalized Fr"ohlich model incorporating SOC and provides comprehensive first-principles analysis of SOC effects on ZPR in cubic semiconductors and insulators.

Findings

SOC reduces ZPR by up to 30% in studied materials

Valence band edge modifications mainly drive SOC effects on ZPR

The generalized Fr"ohlich model accurately estimates SOC-induced changes

Abstract

The electronic structure of semiconductors and insulators is affected by ionic motion through electron-phonon interaction, yielding temperature-dependent band gap energies and zero-point renormalization (ZPR) at absolute zero temperature. For polar materials, the most significant contribution to the band gap ZPR can be understood in terms of the Fr\"ohlich model, which focuses on the nonadiabatic interaction between an electron and the macroscopic electrical polarization created by a long-wavelength optical longitudinal phonon mode. On the other hand, spin-orbit interaction (SOC) modifies the bare electronic structure, which will, in turn, affect the electron-phonon interaction and the ZPR. We present a comparative investigation of the effect of SOC on the band gap ZPR of twenty semiconductors and insulators with cubic symmetry using first-principles calculations. We observe a SOC-induced decrease of the ZPR, up to 30%, driven by the valence band edge, which almost entirely originates from the modification of the bare electronic eigenenergies and the decrease of the hole effective masses near the $\Gamma$ point. We also incorporate SOC into a generalized Fr\"ohlich model, addressing the Dresselhaus splitting which occurs in noncentrosymmetric materials, and confirm that the predominance of nonadiabatic effects on the band gap ZPR of polar materials is unchanged when including SOC. Our generalized Fr\"ohlich model with SOC provides a reliable estimate of the SOC-induced decrease of the polaron formation energy obtained from first principles and brings to light some fundamental subtleties in the numerical evaluation of the effective masses with SOC for noncentrosymmetric materials. We finally warn about a possible breakdown of the parabolic approximation within the physically relevant energy range of the Fr\"ohlich interaction for materials with high phonon frequencies treated with SOC.