Vortex lattice for a holographic superconductor

TL;DR

This paper models vortex lattices in a (2+1)-dimensional holographic superconductor, demonstrating that the triangular Abrikosov lattice minimizes free energy similarly to traditional Ginzburg-Landau theory.

Contribution

It provides a holographic realization of vortex lattices, extending the understanding of superconductivity in strongly coupled systems near phase transitions.

Findings

Vortex lattice solutions are obtained perturbatively near the second-order phase transition.

The vortex lattice has lower free energy than the normal state below a critical magnetic field.

The triangular lattice is the most thermodynamically favorable configuration.

Abstract

We investigate the vortex lattice solution in a (2+1)-dimensional holographic model of superconductors constructed from a charged scalar condensate. The solution is obtained perturbatively near the second-order phase transition and is a holographic realization of the Abrikosov lattice. Below a critical value of magnetic field, the solution has a lower free energy than the normal state. Both the free energy density and the superconducting current are expressed by nonlocal functions, but they reduce to the expressions in the Ginzburg-Landau (GL) theory at long wavelength. As a result, a triangular lattice becomes the most favorable solution thermodynamically as in the GL theory of type II superconductors.