Reconciling scaling of the optical conductivity of cuprate superconductors with Planckian resistivity and specific heat

Abstract

Materials tuned to a quantum critical point display universal scaling properties as a function of temperature $T$ and frequency $\omega$. A long-standing puzzle regarding cuprate superconductors has been the observed power-law dependence of optical conductivity with an exponent smaller than one, in contrast to $T$-linear dependence of the resistivity and $\omega$-linear dependence of the optical scattering rate. Here, we present and analyze resistivity and optical conductivity of La${}_{2-x}$Sr${}_x$CuO${}_4$ with $x=0.24$. We demonstrate $\hslash \omega /k_{\mathrm{B}}T$ scaling of the optical data over a wide range of frequency and temperature, $T$-linear resistivity, and optical effective mass proportional to $\sim \ln T$ corroborating previous specific heat experiments. We show that a $T,\omega$-linear scaling Ansatz for the inelastic scattering rate leads to a unified theoretical description of the experimental data, including the power-law of the optical conductivity. This theoretical framework provides new opportunities for describing the unique properties of quantum critical matter.

Accepted version

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