Heat transport in insulators from ab initio Green-Kubo theory

TL;DR

This paper introduces a gauge-invariant approach and a new data analysis method to accurately compute heat transport in insulators using ab initio Green-Kubo theory, overcoming previous theoretical and computational challenges.

Contribution

It establishes a gauge invariance principle for energy flux in Density-Functional Theory and proposes a statistical analysis technique to reduce simulation time for thermal conductivity calculations.

Findings

Validated the gauge invariance principle for energy flux.

Demonstrated reduced simulation times with the new data analysis method.

Applied the approach to classical and quantum simulations of insulators.

Abstract

The Green-Kubo theory of thermal transport has long be considered incompatible with modern simulation methods based on electronic-structure theory, because it is based on such concepts as energy density and current, which are ill-defined at the quantum-mechanical level. Besides, experience with classical simulations indicates that the estimate of heat-transport coefficients requires analysing molecular trajectories that are more than one order of magnitude longer than deemed feasible using ab initio molecular dynamics. In this paper we report on recent theoretical advances that are allowing one to overcome these two obstacles. First, a general gauge invariance principle has been established, stating that thermal conductivity is insensitive to many details of the microscopic expression for the energy density and current from which it is derived, thus permitting to establish a rigorous expression for the energy flux from Density-Functional Theory, from which the conductivity can be computed in practice. Second, a novel data analysis method based on the statistical theory of time series has been proposed, which allows one to considerably reduce the simulation time required to achieve a target accuracy on the computed conductivity. These concepts are illustrated in detail, starting from a pedagogical introduction to the Green-Kubo theory of linear response and transport, and demonstrated with a few applications done with both classical and quantum-mechanical simulation methods.