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  • Letter
  • Open Access

Holographic Abrikosov lattice: Vortex matter from black hole

Chuan-Yin Xia1,*, Hua-Bi Zeng1,†, Yu Tian2,3,‡, Chiang-Mei Chen4,§, and Jan Zaanen5,∥

  • 1Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
  • 2School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China
  • 3Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 4Department of Physics, Center for High Energy and High Field Physics (CHiP), National Central University, Chungli 32001, Taiwan
  • 5Institute Lorentz for Theoretical Physics, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands

  • *chuanyinxia@foxmail.com
  • †hbzeng@yzu.edu.cn
  • ‡ytian@ucas.ac.cn
  • §cmchen@phy.ncu.edu.tw
  • ∥jan@lorentz.leidenuniv.nl
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Phys. Rev. D 105, L021901 – Published 4 January, 2022

DOI: https://doi.org/10.1103/PhysRevD.105.L021901

Abstract

The AdS/CFT correspondence provides a unique way to study the vortex matter phases in superconductors. We solve the dynamical evolution of a superconductor in 2+1 dimensions at a finite temperature subjected to a magnetic field quench in terms of a gravitational “hairy black hole” dual living in an asymptotic AdS4 space. We exploit this to determine the nature of the equilibrium states realized at long times after the quench of this two dimensional type II superconductor in a perpendicular external uniform magnetic field B0. This holographic superconductor exhibits the generic lower (Bc1(T)) and upper (Bc2(T)) critical fields. For B0<Bc1(T) the magnetic field is completely expelled revealing the Meissner phase, while the superconductivity is destroyed when B0>Bc2(T). Abrikosov lattices appear in the range Bc1(T)<B0<Bc2(T) that realize various configurations in the form of hexagonal, square and slightly irregular square lattices pending the magnetic field strength and the influence of finite size boundaries. We show this to be consistent with the expectations of Ginzburg-Landau theory where the upper and lower critical fields are associated with the inverse squares of the coherence length and magnetic penetration depth, respectively.

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Outline

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Phys. Rev. D 105, L021901– Published 4 January, 2022
  • Received 30 November 2021
  • Accepted 20 December 2021
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