Full Counting Statistics of Phonon Transport in Disordered Systems

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.

11 pages, 8 figures

References in corpus (9)

• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Quantum thermal transport in nanostructures
• Full-counting statistics of charge and spin transport in the transient regime: A nonequilibrium Green's function approach
• Full-counting statistics of transient energy current in mesoscopic systems
• Transport and localization in a topological phononic lattice with correlated disorder
• Valley filtering effect of phonons in graphene with a grain boundary
• Phonon localization in binary alloys with diagonal and off-diagonal disorder: A cluster Green's function approach
• Short time dynamics of molecular junctions after projective measurement
• Phonon transport in a one-dimensional harmonic chain with long-range interaction and mass disorder