Gapless superconductivity and string theory

Abstract

Coexistence of superconducting and normal components in nanowires at currents below the critical (a "mixed" state) would have important consequences for the nature and range of potential applications of these systems. For clean samples, it represents a genuine interaction effect, not seen in the mean-field theory. Here we consider properties of such a state in the gravity dual of a strongly coupled superconductor constructed from D3 and D5 branes. We find numerically uniform gapless solutions containing both components but argue that they are unstable against phase separation, as their free energies are not convex. We speculate on the possible nature of the resulting non-uniform sate ("emulsion") and draw analogies between that state and the familiar mixed state of a type II superconductor in a magnetic field.