Conductivities in an anisotropic medium

TL;DR

This paper models anisotropic condensed matter systems using a gravity dual with anisotropic black holes, analyzing how anisotropy affects electric, thermoelectric, and thermal conductivities, revealing Drude peaks and power law behaviors.

Contribution

It introduces a gravity model with anisotropic black holes to study how anisotropy influences linear response conductivities in condensed matter analogs.

Findings

Electric conductivity shows a Drude peak at low frequency.

Power law behavior in intermediate frequency regime varies with anisotropy.

Maximum DC conductivity occurs at a critical anisotropy value.

Abstract

In order to imitate anisotropic medium of a condensed matter system, we take into account an Einstein-Maxwell-dilaton-axion model as a dual gravity theory where the anisotropy is caused by different momentum relaxations. This gravity model allows an anisotropic charged black hole solution. On this background, we investigate how the linear responses of vector modes like electric, thermoelectric, and thermal conductivities rely on the anisotropy. We find that the electric conductivity in low frequency limit shows a Drude peak and that in the intermediate frequency regime it reveals the power law behavior. Especially, when the anisotropy increases the exponent of the power law becomes smaller. In addition, we find that there exist a critical value for the anisotropy at which the DC conductivity reaches to its maximum value.