Isolated vortex and vortex lattice in a holographicp-wave superconductor

Abstract

Using the holographic gauge-gravity duality, we find a solution for an isolated vortex and a vortex lattice in a $2+1$-dimensional $p$-wave superconductor, which is described by the boundary theory dual to an $SU(2)$ gauge theory in $3+1$-dimensional anti-de Sitter space. Both ${p}_{x}+i{p}_{y}$ and ${p}_{x}\ensuremath{-}i{p}_{y}$ components of the superconducting order parameter, as well as the effects of a magnetic field on these components, are considered. The isolated vortex solution is studied, and it is found that the two order parameter components have different amplitudes due to the time-reversal symmetry breaking. The vortex lattice for large magnetic fields is also studied, where it is argued that only one order parameter component will be nonzero sufficiently close to the upper critical field. The upper critical field exhibits a characteristic upward curvature, reflecting the effects of field-induced correlations captured by the holographic theory. The free energy is calculated perturbatively in this region of the phase diagram, and it is shown that the triangular vortex lattice is the thermodynamically preferred solution.