Microscopic formulas for thermoelectric transport coefficients in lattice systems

TL;DR

This paper derives unambiguous microscopic formulas for thermoelectric transport coefficients in lattice systems, clarifying the role of additional terms and the interpretation of tensor components.

Contribution

It provides a new version of Kubo formulas for lattice systems that resolves ambiguities present in textbook definitions, with conditions for when additional terms vanish.

Findings

Additional terms in formulas vanish for symmetric tensor components in certain lattice systems.

Skew-symmetric components are meaningful only as relative differences between materials.

A natural choice of energy current simplifies the formulas in many cases.

Abstract

A macroscopic description of thermoelectric phenomena involves several tensorial transport coefficients. Textbook microscopic Kubo formulas for them are plagued with ambiguities in the definitions of the current operators and the magnetization. We derive a version of these formulas for lattice systems which is free from ambiguities but contains additional terms compared to the textbook results. For symmetric components of thermoelectric tensors, we identify a large class of lattice systems for which the additional terms vanish with a natural choice of the energy current. To eliminate ambiguities in the skew-symmetric components, one needs to interpret them as relative quantities: only their differences for pairs of materials are well-defined.