The Microscopic Response Method: theory of transport for systems with both topological and thermal disorder

TL;DR

This paper reviews and advances the Microscopic Response Method for calculating transport properties in complex disordered systems, emphasizing temperature dependence and practical computation compared to traditional formalisms.

Contribution

It develops the Microscopic Response Method to include topological and thermal disorder effects, providing a practical alternative to the Kubo formalism for transport calculations.

Findings

Derived conductivity and Hall mobility for amorphous semiconductors and polymers.

Included effects of quantized lattice vibrations on transport coefficients.

Presented a diagrammatic expansion for higher-order process contributions.

Abstract

In this paper, we review and substantially develop the recently proposed "Microscopic Response Method", which has been devised to compute transport coefficients and especially associated temperature dependence in complex materials. The conductivity and Hall mobility of amorphous semiconductors and semiconducting polymers are systematically derived, and shown to be more practical than the Kubo formalism. The effect of a quantized lattice (phonons) on transport coefficients is fully included and then integrated out, providing the primary temperature dependence for the transport coefficients. For higher-order processes, using a diagrammatic expansion, one can consistently include all important contributions to a given order and directly write out the expressions of transport coefficients for various processes.