Scaling theory of the cuprate strange metals

TL;DR

Cuprate strange metals show anomalous transport scaling not explained by quasiparticles. The authors propose a minimal quantum critical scaling framework based on covariant current scaling with three exponents $z$, $\theta$, and $\Phi$, inspired by holographic theories, to organize transport and thermodynamics. From three core transport criteria, they fix the exponents to $z=4/3$, $\theta=0$, $\Phi=-2/3$, and show that the temperature dependences of $\rho_{xx}$, the Hall angle, the Hall Lorenz ratio, magnetoresistance, and thermopower are captured; they also derive predictions for $\kappa_{xx}$, the Nernst coefficient, and thermodynamic quantities $c$ and $\chi$. The framework thus provides a unified, non-quasiparticle description of strange metal transport and offers constraints for microscopic theories and a guide for future experiments and the understanding of high-temperature superconductivity.

Abstract

We show that the anomalous temperature scaling of five distinct transport quantities in the strange metal regime of the cuprate superconductors can be reproduced with only two nontrivial critical exponents. The quantities are: (i) the electrical resistivity, (ii) the Hall angle, (iii) the Hall Lorenz ratio, (iv) the magnetoresistance and (v) the thermopower. The exponents are the dynamical critical exponent z = 4/3 and an anomalous scaling dimension Phi = -2/3 for the charge density operator.

Figures (1)

• Figure 1: Thermopower versus temperature for LSCO at doping $x= 0.25$, over temperatures $250 - 700K$. Dots are taken from the data curve in thermo0. The blue line is a fit to $S \sim - b \, T^{1/2} + a$, and goes right through the data points. In contrast, fits to $S \sim - b \, T + a$ (orange line) and $S \sim b \, T^{-1/2} + a$ (green line) do not fit the data well.