Conductivity of Strongly Coupled Striped Superconductor

TL;DR

Using gauge/gravity duality, the paper analyzes the conductivity of a strongly coupled striped superconductor in the large modulation limit, where backreaction is neglected. It finds that the optical conductivity is spatially inhomogeneous but isotropic at low $T$, while near $T_c$ it becomes inhomogeneous and anisotropic with an imaginary part that scales as $1/\omega$; analytic expressions are derived for the low-frequency conductivity parallel to the stripes and, for general scaling dimension $\Delta$, for the perpendicular direction, revealing AC/DC anisotropic responses and a delta-function DC conductivity signaling superconductivity. The study also computes the speed of the second sound $v=\sqrt{C}\,\langle O_{\Delta}\rangle^{(0)}$ and the thermodynamic susceptibility, showing how broken translational symmetry in one direction drives the observed anisotropy. These results shed light on how stripe order and strong coupling shape transport properties and offer qualitative benchmarks for experimental systems with anisotropic superconductivity.

Abstract

We study the conductivity of a strongly coupled striped superconductor using gauge/gravity duality (holography). The study is done analytically, in the large modulation regime. We show that the optical conductivity is inhomogeneous but isotropic at low temperatures. Near but below the critical temperature, we calculate the conductivity analytically at small frequency ω, and find it to be both inhomogeneous and anisotropic. The anisotropy is imaginary and scales like 1/ω. We also calculate analytically the speed of the second sound and the thermodynamic susceptibility.