Holographic Abrikosov lattice: vortex matter from black hole

TL;DR

This paper uses holographic duality to study vortex lattice phases in a strongly coupled superconductor, revealing critical magnetic fields and various lattice configurations consistent with known physical laws.

Contribution

It introduces a holographic model for vortex matter in superconductors, solving nonlinear equations to identify critical fields and lattice structures.

Findings

Identified two critical magnetic fields, B_{c1}(T) and B_{c2}(T).

Observed various vortex lattice configurations including hexagonal and square lattices.

Confirmed that critical fields scale inversely with coherence length and penetration depth.

Abstract

The AdS/CFT correspondence provides a unique way to study the vortex matter phases in superconductors. We solved the nonlinear equations of motion for the Abelain-Higgs theory living on the AdS$_4$ black hole boundary that is dual to a two dimensional strongly coupled type II superconductor at temperature $T$ with a perpendicular external uniform magnetic field $B_0$. We found the associated two critical magnetic fields, $B_{c1}(T)$ and $B_{c2}(T)$. For $B_0 < B_{c1}(T)$ the magnetic field will be expelled out by the superconductor resembling the Meissner effect and the superconductivity will be destroyed when $B_0 > B_{c2}(T)$. The Abrikosov lattice appears in the range $B_{c1}(T) < B_0 < B_{c2}(T)$ including, due to the finite size and boundary effect, several kinds of configurations such as hexagonal, square and slightly irregular square lattices, when the magnetic field is increased. The upper and lower critical fields behave as inverse squares of coherence length and magnetic penetration depth respectively which matches the well known consensus.