DC conductivity with external magnetic field in hyperscaling violating geometry

Abstract

We investigate the holographic DC conductivity of (2+1) dimensional systems while considering hyperscaling violating geometry in bulk. We consider Einstein-Maxwell-Dilaton system with two gauge fields and Liouville type potential for dilaton. We also consider axionic fields in bulk to introduce momentum relaxation in the system. We apply an external magnetic field to study the response of the system and obtain analytic expressions for DC conductivity, Hall angle and (thermo)electric conductivity.

Hyperscaling violating geometry with magnetic field and DC conductivity

“…these expressions,after setting θ = 1 − z, agree with the results obtained in [21] using the near horizon method.…”

“…This analysis can accommodate different boundary coditions which may lead to different behaviour of thermal conductivities. In the present case, we have used Dirichlet boundary condition on spatial components of one of the gauge fields and find agreement of conductivities derived in approach of near horizon analysis [21]. We have discussed temperature dependence of thermoelectric cunductivities and Hall angle in several scaling regimes.…”

Thermoelectric DC conductivities in hyperscaling violating Lifshitz theories

“…An exact asymptotically hyperscaling violating black brane solution of (2.12) with non-zero axion charge was presented in [15] (see also [18,17]) for the case d s = 2 and generic exponents z and θ, subject to a number of conditions that we will specify shortly. This solution exists when the expressions (2.14) hold exactly, instead of merely asymptotically near the UV.…”

“…with the normalization of the dilaton kinetic term in (2.1) chosen such that α = 1/2. The exact black brane solution discussed in [15,17] then takes the form 5…”

“…The electrical DC conductivity matrix for this model was computed originally in [15], using the near horizon analysis of [16]. Subsequently, [17] computed the full thermoelectric conductivity matrix in the presence of a background magnetic field, using the same near horizon analysis. 4 However, the near horizon analysis does not suffice to identify the conserved currents in the dual 4 See also [18,19].…”