Electro Thermal Transport Coefficients at Finite Frequencies

TL;DR

This paper reviews a formalism for calculating thermoelectric coefficients at finite frequencies in correlated materials, using exact diagonalization for models like Hubbard and t-J, and applies it to sodium cobaltate with predictions for new materials.

Contribution

It introduces a generalized transport formalism at finite frequencies and demonstrates its application to strongly correlated models and real materials.

Findings

Exact finite frequency transport coefficients computed for Hubbard and t-J models.

Benchmarking of approximation methods against exact diagonalization results.

Predictions for thermoelectric behavior in sodium cobaltate and potential new materials.

Abstract

We review a recently developed formalism for computing thermoelectric coefficients in correlated matter. The usual difficulties of such a calculation are circumvented by a careful generalization the transport formalism to finite frequencies, from which one can extract the high frequency objects. The technical parallel between the Hall constant and the Seebeck coefficient is explored and used to advantage. For small clusters, exact diagonalization gives the full spectrum for the Hubbard and especially the $t$-$J$ model, a prototypical model for strong correlations, and this spectrum can be used to compute the exact finite frequency transport coefficients and hence to benchmark various approximations. An application of this formalism to the physically important case of sodium cobaltate $Na_xCoO_2$ is made, and interesting predictions for new materials are highlighted.