Holographic duality and the resistivity of strange metals

TL;DR

This paper addresses the puzzling linear resistivity observed in strange metals by proposing a hydrodynamic mechanism: a strongly interacting quantum critical fluid with minimal viscosity, when weakly coupled to quenched disorder, acquires a viscous contribution to momentum relaxation that makes the DC resistivity scale with the electronic entropy, $\rho_{DC}(T) \sim \eta(T) \sim S_e(T)$. The authors derive this result rigorously via the memory-matrix formalism and then realize it in a controlled holographic model of a locally quantum critical state (z $\to$ $\infty$) described by a dual Einstein-Maxwell-Dilaton gravity theory, with near-horizon AdS$_2\times$R$^2$ geometry ensuring $s\sim T$. They further show how explicit momentum dissipation, either via weak disorder or a graviton mass term, yields a nonzero $\rho_{DC}$ that remains linear in $T$ at low temperatures, aligning with cuprate phenomenology. The work predicts testable signatures, such as a correlation between $\rho_{DC}$ and $s(T)$ and potential violations of the Wiedemann–Franz law, while also clarifying limitations (e.g., Hall angle) and guiding experimental scrutiny of hydrodynamic transport in strongly correlated metals.

Abstract

We present a strange metal, described by a holographic duality, which reproduces the famous linear resistivity of the normal state of the copper oxides, in addition to the linear specific heat. This holographic metal reveals a simple and general mechanism for producing such a resistivity, which requires only quenched disorder and a strongly interacting, locally quantum critical state. The key is the minimal viscosity of the latter: unlike in a Fermi-liquid, the viscosity is very small and therefore is important for the electrical transport. This mechanism produces a resistivity proportional to the electronic entropy.