General relativity and the cuprates

Abstract

We add a periodic potential to the simplest gravitational model of a superconductor and compute the optical conductivity. In addition to a superfluid component, we find a normal component that has Drude behavior at low frequency followed by a power law fall-off. Both the exponent and coefficient of the power law are temperature independent and agree with earlier results computed above T c. These results are in striking agreement with measurements on some cuprates. We also find a gap Δ = 4.0 T c, a rapidly decreasing scattering rate, and "missing spectral weight" at low frequency, all of which also agree with experiments. © 2013 SISSA, Trieste, Italy.