Theory of temperature dependent phonon-renormalized properties

TL;DR

This paper develops a harmonic theory for how phonon-related properties of solids change with temperature, introducing new extrapolation schemes and analyzing low-temperature behavior across different dimensions.

Contribution

It introduces a perturbation theory for phonon-phonon interactions and two novel schemes for more accurate zero-point correction extrapolation.

Findings

New schemes improve zero-point correction accuracy by an order of magnitude

Derivation of temperature dependence laws: T^4 in 3D, T^2 in 2D, T^{3/2} in 1D

General harmonic framework applicable to various phonon-renormalized properties

Abstract

We present a general harmonic theory for the temperature dependence of phonon-renormalized properties of solids. Firstly, we formulate a perturbation theory in phonon-phonon interactions to calculate the phonon renormalization of physical quantities. Secondly, we propose two new schemes for extrapolating phonon zero-point corrections from temperature dependent data that improve the accuracy by an order of magnitude compared to previous approaches. Finally, we consider the low-temperature limit of the class of observables that includes the electronic band gap, obtaining a $T^4$ dependence in three dimensions, $T^2$ in two dimensions, and $T^{3/2}$ in one dimension.