General Relativity and the Cuprates

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 $\mathrm{\Delta }=4.0T_c$, a rapidly decreasing scattering rate, and “missing spectral weight” at low frequency, all of which also agree with experiments.