Reconciling scaling of the optical conductivity of cuprate superconductors with Planckian resistivity and specific heat
B. Michon, Christophe Berthod, Carl Willem Rischau, Amirreza Ataei, Lu Chen, Seiki Komiya, Shimpei Ono, Louis Taillefer, D. van der Marel, Antoine Georges
Abstract
Abstract 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 $$\sim \ln T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>~</mml:mo> <mml:mo>ln</mml:mo> <mml:mi>T</mml:mi> </mml:math> 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.