Anomalous scalings of the cuprate strange metals from nonlinear electrodynamics

Abstract: We examine transport in a holographic model which describes, through a nonlinear gauge field sector, generic nonlinear interactions between the charge carriers. Scaling exponents are introduced by using geometries which are nonrelativistic and hyperscaling-violating in the infrared. In the dilute charge limit in which the gauge field sector does not backreact on the geometry, a particularly simple nonlinear theory reproduces the anomalous temperature dependence of the resistivity and Hall angle of the cuprate strange metals, $R \sim T$ and $\cot\Theta_H \sim T^2$ while also allowing for a linear entropy $S \sim T$, and predicts that the magnetoresistance for small values of the magnetic field $h$ should scale as $\sim h^2 T^{-4}$. Our study lends evidence to the idea that the strange metal behavior of the cuprates relies crucially on the linear temperature dependence of the entropy.