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

Materials tuned to a quantum critical point display universal scaling properties as a function of temperature T and frequency ω. 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 ω-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 ℏω/k B T scaling of the optical data over a wide range of frequency and temperature, T-linear resistivity, and optical effective mass proportional to [Formula: see text] corroborating previous specific heat experiments. We show that a T, ω-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.