A Striped Holographic Superconductor

TL;DR

This paper models inhomogeneous holographic superconductors with charge density waves, showing that superconducting stripes form below a critical temperature and analyzing their properties and conductivity.

Contribution

It introduces a holographic model of superconductivity with charge density waves, demonstrating the formation of superconducting stripes and their thermodynamic stability.

Findings

Superconducting stripes develop below a critical temperature.

The critical temperature depends on the modulation wave vector.

Conductivity along the stripes was computed.

Abstract

We study inhomogeneous solutions of a 3+1-dimensional Einstein-Maxwell-scalar theory. Our results provide a holographic model of superconductivity in the presence of a charge density wave sourced by a modulated chemical potential. We find that below a critical temperature superconducting stripes develop. We show that they are thermodynamically favored over the normal state by computing the grand canonical potential. We investigate the dependence of the critical temperature on the modulation's wave vector, which characterizes the inhomogeneity. We find that it is qualitatively similar to that expected for a weakly coupled BCS theory, but we point out a quantitative difference. Finally, we use our solutions to compute the conductivity along the direction of the stripes.