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 ℏ ω / 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 ~ ln T ~ ln T 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.