General Relativity and the Cuprates

TL;DR

This paper models high-temperature superconductors using a gravitational approach, revealing optical conductivity features that match experimental observations in cuprates, including a superfluid component and characteristic spectral behaviors.

Contribution

It introduces a gravitational model with a periodic potential to replicate key optical properties of cuprate superconductors, providing a novel theoretical framework.

Findings

Normal component exhibits Drude behavior at low frequency

Power law fall-off in conductivity with temperature-independent exponent

Spectral features such as gap and missing spectral weight match experiments

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