Notes on Properties of Holographic Strange Metals

TL;DR

This paper analyzes holographic strange metals in various dimensions using Lifshitz black holes, deriving analytical results for thermodynamic and transport properties, and clarifying conditions for linear resistivity characteristic of strange metals.

Contribution

It provides new analytical results for thermodynamics and conductivities of holographic strange metals, including universal forms and conditions for linear resistivity.

Findings

Exact free energy, entropy density, and heat capacity in Lifshitz backgrounds.

Universal DC and Hall conductivities in large density limit.

Conditions for linear temperature dependence of resistivity.

Abstract

We investigate properties of holographic strange metals in $p+2$-dimensions, generalizing the analysis performed in arXiv:0912.1061. The bulk spacetime is $p+2$-dimensional Lifshitz black hole, while the role of charge carriers is played by probe D-branes. We mainly focus on massless charge carriers, where most of the results can be obtained analytically. We obtain exact results for the free energy and calculate the entropy density, the heat capacity as well as the speed of sound at low temperature. We obtain the DC conductivity and DC Hall conductivity and find that the DC conductivity takes a universal form in the large density limit, while the Hall conductivity is also universal in all dimensions. We also study the resistivity in different limits and clarify the condition for the linear dependence on the temperature, which is a key feature of strange metals. We show that our results for the DC conductivity are consistent with those obtained via Kubo formula and we obtain the charge diffusion constant analytically. The corresponding properties of massive charge carriers are also discussed in brief.