Verification and Validation of zero-point electron-phonon renormalization of the bandgap, mass enhancement, and spectral functions

TL;DR

This paper rigorously compares multiple first-principles computational methods and software for verifying electron-phonon interactions, focusing on bandgap renormalization, mass enhancement, and spectral functions in solid-state physics.

Contribution

It provides a comprehensive validation of different first-principles codes and methods, highlighting their agreement and differences in electron-phonon property calculations.

Findings

Excellent agreement between codes using the same formalism.

Good agreement between DFPT and Wannier function perturbation methods.

Momentum dependence of the Debye-Waller term affects mass enhancement calculations.

Abstract

Verification and validation of methods and first-principles software are at the core of computational solid-state physics but are too rarely addressed. We compare four first-principles codes: Abinit, Quantum ESPRESSO, EPW, ZG, and three methods: (i) the Allen-Heine-Cardona theory using density functional perturbation theory (DFPT), (ii) the Allen-Heine-Cardona theory using Wannier function perturbation theory (WFPT), and (iii) an adiabatic non-perturbative frozen-phonon method. For these cases, we compute the real and imaginary parts of the electron-phonon self-energy in diamond and BAs, including dipoles and quadrupoles when interpolating. We find excellent agreement between software that implements the same formalism as well as good agreement between the DFPT and WFPT methods. Importantly, we find that the Deybe-Waller term is momentum dependent which impacts the mass enhancement, yielding approximate results when using the Luttinger approximations. Finally, we compare the electron-phonon spectral functions between Abinit and EPW and find excellent agreement even away from the band edges.