Charged Dilatonic Black Holes and their Transport Properties

TL;DR

This paper explores the transport properties of charged dilatonic black holes within holographic theories, analyzing how their resistivity and conductivity scale with temperature and frequency across different parameter regimes.

Contribution

It provides a detailed analysis of the IR dynamics and transport behaviors of dilatonic black holes, identifying conditions for linear resistivity and Mott-like insulating phases.

Findings

DC resistivity can be linear in temperature in certain parameter regions.

Resistivity scales with heat capacity and entropy for non-dilaton scalar operators.

Finite density theories can exhibit Mott-like insulating behavior.

Abstract

We briefly explain the consistency conditions imposed on the effective holographic theories, which are parameterized by two real exponents $(\gamma,\delta)$ that control the IR dynamics. The general scaling of DC resistivity with temperature at low temperature and AC conductivity at low frequency across the whole $(\gamma,\delta)$ plane are explained. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for $(2+1)$-dimensional systems. Regions are identified where the theory at finite density is a Mott-like insulator. This contribution is based on arXiv:1005.4690 with emphasis on the transport properties of charged dilatonic black holes with potential.