Holographic Conductivity for Logarithmic Charged Dilaton-Lifshitz Solutions

TL;DR

This paper investigates how logarithmic nonlinear electrodynamics influences the holographic conductivity of Lifshitz dilaton black holes, revealing conditions under which conductivity exists and its frequency-dependent behavior, with implications for condensed matter systems.

Contribution

It introduces the effects of logarithmic nonlinear electrodynamics on holographic conductivity in Lifshitz dilaton backgrounds, highlighting the dependence on the dynamical exponent z and frequency.

Findings

Conductivity exists for z ≤ 3 and vanishes for z > 3.

Real part of conductivity is identical at specific frequencies for AdS and Lifshitz cases.

Large frequency behavior differs between Lifshitz and AdS, indicating additional charge carriers.

Abstract

We disclose the effects of the logarithmic nonlinear electrodynamics on the holographic conductivity of Lifshitz dilaton black holes/branes. We analyze thermodynamics of these solutions as a necessary requirement for applying gauge/gravity duality, by calculating conserved and thermodynamic quantities such as the temperature, entropy, electric potential and mass of the black holes/branes. We calculate the holographic conductivity for a $(2+1)$-dimensional brane boundary and study its behavior in terms of the frequency per temperature. Interestingly enough, we find out that, in contrast to the Lifshitz-Maxwell-dilaton black branes which has conductivity for all $z$, here in the presence of nonlinear gauge field, the holographic conductivity do exist provided $z\leq3$ and vanishes for $z>3$. It is shown that independent of the nonlinear parameter $\beta$, the real part of the conductivity is the same for a specific value of frequency per temperature in both AdS and Lifshitz cases. Besides, the behavior of real part of conductivity for large frequencies has a positive slope with respect to large frequencies for a system with Lifshitz symmetry whereas it tends to a constant for a system with AdS symmetry. This behavior may be interpreted as existence of an additional charge carrier rather than the AdS case, and is due to the presence of the scalar dilaton field in model. Similar behavior for optical conductivity of single-layer graphene induced by mild oxygen plasma exposure has been reported.