Disordered Crystals from First Principles II: Transport Coefficients

TL;DR

This paper develops a first-principles computational framework combining ab-initio molecular dynamics and a finite-temperature Kubo-formula to accurately predict electron transport properties in thermally disordered crystals, demonstrated on silicon.

Contribution

It introduces a covariant atomic-orbital formalism and an optimal finite-volume approximation for the Kubo-formula, enabling more accurate and efficient transport coefficient calculations in disordered crystals.

Findings

Transport coefficients of silicon calculated at various temperatures.

Demonstration of the covariance-preserving formalism.

Implementation of numerical innovations for longer AIMD simulations.

Abstract

This is the second part of a project on the foundations of first-principle calculations of the electron transport in crystals at finite temperatures, aiming at a predictive first-principles platform that combines ab-initio molecular dynamics (AIMD) and a finite-temperature Kubo-formula with dissipation for thermally disordered crystalline phases. The latter are encoded in an ergodic dynamical system $(\Omega,\mathbb G,{\rm d}\mathbb P)$, where $\Omega$ is the configuration space of the atomic degrees of freedom, $\mathbb G$ is the space group acting on $\Omega$ and ${\rm d}\mathbb P$ is the ergodic Gibbs measure relative to the $\mathbb G$-action. We first demonstrate how to pass from the continuum Kohn-Sham theory to a discrete atomic-orbitals based formalism without breaking the covariance of the physical observables w.r.t. $(\Omega,\mathbb G,{\rm d}\mathbb P)$. Then we show how to implement the Kubo-formula, investigate its self-averaging property and derive an optimal finite-volume approximation for it. We also describe a numerical innovation that made possible AIMD simulations with longer orbits and elaborate on the details of our simulations. Lastly, we present numerical results on the transport coefficients of crystal silicon at different temperatures.