DC and Hall conductivity in holographic massive Einstein-Maxwell-Dilaton gravity

Zhenhua Zhou,Jian-Pin Wu,Yi Ling

doi:10.1007/jhep08(2015)067

Abstract

We investigate the holographic DC and Hall conductivity in massive Einstein-Maxwell-Dilaton (EMD) gravity. Two special EMD backgrounds are considered explicitly. One is dyonic Reissner-Nordstr$\ddot{o}$m-AdS (RN-AdS) geometry and the other one is hyperscaling violation AdS (HV-AdS) geometry. We find that the linear-T resistivity and quadratic-T inverse Hall angle can be simultaneously achieved in HV-AdS models, providing a hint to construct holographic models confronting with the experimental data of strange metal in future.

Highlights

Inspired by the work in [23], in present paper we attempt to address this dichotomy between resistivity and the Hall angle in a simpler holographic framework, i.e., massive gravity
We find that the linear-T resistivity and quadraticT inverse Hall angle can be simultaneously achieved in hyperscaling violation AdS (HV-AdS) models, providing a hint to construct holographic models confronting with the experimental data of strange metal in future
In this paper we have presented a mechanism to implement the dichotomy between the DC resistivity and the Hall angle in massive EMD gravity theory, where the diffeomorphism symmetry is broken along spatial directions and the momentum of the system has dissipation

Summary

DC and Hall conductivity in holographic massive EMD gravity

We shall derive general analytic expressions for DC and Hall conductivity in holographic massive gravity, which can be applicable for a large class of scaling geometries. A similar result has been reported in [23], in which a Q-lattice is introduced instead of massive term to dissipate the momentum It has been shown by Andrade and Withers in [37] that the conductivity in massive gravity is equivalent to that of a linear axion model, which could be viewed as a special case of Q-lattices. In this circumstance, one needs to fix either the chemical potential or the charge density of the system. From a phenomenological point of view we intend to perform the analysis with a fixed charge density since most of the experimental setup for cuprates are at constant charge density, for instance, as described in [56]

DC and Hall conductivity in some specific holographic models

DC and Hall conductivity in dyonic HV-AdS geometry

Conclusions and discussions

A The dyonic HV-AdS solution of massive EMD gravity