Coherent/incoherent metal transition in a holographic model

TL;DR

This paper investigates the AC electric, thermoelectric, and thermal conductivities in a holographic model with momentum relaxation, identifying conditions for coherent and incoherent metallic behavior and analyzing their frequency-dependent properties.

Contribution

It provides an analytical description of modified Drude peaks in holographic metals and explores the presence or absence of scaling laws across different parameter regimes.

Findings

Modified Drude peaks are analytically characterized.

Incoherent metal behavior occurs when eta > mu.

No clear scaling laws are observed in the studied parameter range.

Abstract

We study AC electric($\sigma$), thermoelectric($\alpha$), and thermal($\bar{\kappa}$) conductivities in a holographic model, which is based on 3+1 dimensional Einstein-Maxwell-scalar action. There is momentum relaxation due to massless scalar fields linear to spatial coordinate. The model has three field theory parameters: temperature($T$), chemical potential($\mu$), and effective impurity($\beta$). At low frequencies, if $\beta < \mu$, all three AC conductivities($\sigma, \alpha, \bar{\kappa}$) exhibit a Drude peak modified by pair creation contribution(coherent metal). The parameters of this modified Drude peak are obtained analytically. In particular, if $\beta \ll \mu$ the relaxation time of electric conductivity approaches to $2\sqrt{3} \mu/\beta^2$ and the modified Drude peak becomes a standard Drude peak. If $\beta > \mu$ the shape of peak deviates from the Drude form(incoherent metal). At intermediate frequencies($T<\omega<\mu$), we have analysed numerical data of three conductivities($\sigma, \alpha, \bar{\kappa}$) for a wide variety of parameters, searching for scaling laws, which are expected from either experimental results on cuprates superconductors or some holographic models. In the model we study, we find no clear signs of scaling behaviour.