Holographic Abrikosov lattice: vortex matter from black hole

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.

5 pages,4 figures

References in corpus (5)

• Building an AdS/CFT superconductor
• A Holographic Superconductor in an External Magnetic Field
• Inhomogeneous Structures in Holographic Superfluids: II. Vortices
• Phases of Holographic Superconductors in an External Magnetic Field
• Scanning the Parameter Space of Holographic Superconductors

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• Noncommutative AdS black hole and the IR holographic superconductor
• In-situ Investigation of the Phase Formation and Superconductivity in V${}_3$Si Thin Films at High Temperatures
• Kibble-Zurek Mechanism and Beyond: Lessons from a Holographic Superfluid Disk
• Interior structure of black holes with nonlinear terms
• A new rotating axionic AdS${}_4$ black hole dressed with a scalar field
• Novel five-dimensional rotating Lifshitz black holes with electric and axionic charges
• Effects of background rotation and anisotropy in the holographic description of type-II superconductors