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 $T_c$ 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 $T_c$ on the modulation’s wave vector, which characterizes the inhomogeneity. We find that it is qualitatively similar to that expected for a weakly coupled Bardeen-Cooper-Schrieer theory, but we point out a quantitative difference. Finally, we use our solutions to compute the conductivity along the direction of the stripes.

• Received 16 November 2010

DOI:https://doi.org/10.1103/PhysRevD.83.064009