Holographic DC Conductivity for a Power-law Maxwell Field

TL;DR

This paper derives the holographic DC conductivity for a power-law Maxwell field in a black brane background, revealing phase transitions and diverse conductive behaviors in the dual boundary theory.

Contribution

It provides a novel expression for holographic DC conductivity considering a power-law Maxwell field and explores phase transitions and conductivity behaviors.

Findings

Multiple phases with distinct conductivity properties

Presence of phase transitions indicated by discontinuities in conductivity or its derivatives

Identification of phases with negative magneto-resistance and Mott-like behavior

Abstract

We consider a neutral and static black brane background with a probe power-law Maxwell field. Via the membrane paradigm, an expression for the holographic DC conductivity of the dual conserved current is obtained. We also discuss the dependence of the DC conductivity on the temperature, charge density and spatial components of the external field strength in the boundary theory. Our results show that there might be more than one phase in the boundary theory. Phase transitions could occur where the DC conductivity or its derivatives are not continuous. Specifically, we find that one phase possesses a charge-conjugation symmetric contribution, negative magneto-resistance and Mott-like behavior.