Gapless superconductivity and string theory

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.Comment: 23 pages, 3 figures; references added, published in Nucl. Phys.

Geometry of the momentum space: From wire networks to quivers and monopoles

A new nano--material in the form of a double gyroid has motivated us to study (non-commutative $C^*$ geometry of periodic wire networks and the associated graph Hamiltonians. Here we present the general abstract framework, which is given by certain quiver representations, with special attention to the original case of the gyroid as well as related cases, such as graphene. In these geometric situations, the non- commutativity is introduced by a constant magnetic field and the theory splits into two pieces: commutative and non-commutative, both of which are governed by a $C^*$ geometry. In the non-commutative case, we can use tools such as K-theory to make statements about the band structure. In the commutative case, we give geometric and algebraic methods to study band intersections; these methods come from singularity theory and representation theory. We also provide new tools in the study, using $K$-theory and Chern classes. The latter can be computed using Berry connection in the momentum space. This brings monopole charges and issues of topological stability into the picture.Comment: 31 pages, 4 figure

Critical current of a superconducting wire via gauge/gravity duality

We describe application of the gauge/gravity duality to study of thin superconducting wires at finite current. The large number N of colors of the gauge theory is identified with the number of filled transverse channels in the wire. On the gravity side, the physics is described by a system of D3 and D5 branes intersecting over a line. We consider the ground state of the system at fixed electric current and find that at zero temperature the normal state is always unstable with respect to appearance of a superconducting component. We discuss relation of our results to recent experiments on statistics of the switching current in nanowires.Comment: 4 pages, 1 figur