Full Counting Statistics of Phonon Transport in Disordered Systems

TL;DR

This paper extends the full counting statistics-CPA method to phonon transport in disordered systems, enabling efficient calculation of higher-order cumulants and revealing collective features of phonon currents.

Contribution

It develops a novel FCS-CPA formalism for phonon transport, providing a faster and accurate alternative to brute force methods for disordered materials.

Findings

FCS-CPA accurately matches brute force results for phonon transmission moments.

The method achieves 20 times speedup over traditional approaches.

Reveals collective features of phonon current cumulants.

Abstract

The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calculate up to the $8$-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method. The benchmark shows that the FCS-CPA method achieves $20$ times more speedup ratio. Collective features of phonon current cumulants are also revealed.