The holographic vortex lattice using the circular cell method
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Springer
Received: September Revised: November Accepted: December Published: January
24, 23, 23, 10,
2019 2019 2019 2020
Gianni Tallaritaa and Roberto Auzzib,c a
Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ib´ an ˜ez, Diagonal Las Torres, Santiago 7941169, Chile b Dipartimento di Matematica e Fisica, Universit` a Cattolica del Sacro Cuore, via Musei 41, 25121 Brescia, Italy c INFN, Sezione di Perugia, via A. Pascoli, 06123 Perugia, Italy
E-mail: [email protected], [email protected] Abstract: We investigate vortex lattice solutions in a holographic superconductor model in asymptotically AdS4 spacetime which includes the gravitational backreaction of the vortex. The circular cell approximation, which is known to give a good result for several physical quantities in the Ginzburg-Landau model, is used. The critical magnetic fields and the magnetization curve are computed. The vortex lattice profiles are compared to expectations from the Abrikosov solution in the regime nearby the upper critical magnetic field H2c for which superconductivity is lost. Keywords: Holography and condensed matter physics (AdS/CMT), Solitons Monopoles and Instantons, AdS-CFT Correspondence ArXiv ePrint: 1909.05932
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)056
JHEP01(2020)056
The holographic vortex lattice using the circular cell method
Contents 1
2 Theoretical setting 2.1 The normal state
3 5
3 The 3.1 3.2 3.3
6 6 7 9
vortex lattice Metric ansatz Boundary conditions and solutions The critical magnetic field limit H2c
4 Free energy and magnetization
10
5 Discussion
12
1
Introduction
An important and generic property of higher temperature superconductors is the presence of a strange metal state found just above the superconducting critical temperature. The transport properties of strange metals are very different from the ones of conventional Fermi liquid. In particular, the standard quasi-particle picture does not give a useful description of the physics of the system [1, 2]. An interesting class of models without a quasi-particles description can be built using the AdS/CFT correspondence. The correspondence maps a strongly interacting quantum system in the boundary to a classical gravity problem in the bulk, and so it provides a controlled environment in which to study strongly coupled systems. Since Abrikosov’s seminal work [3], the magnetic properties of type II superconductors have been the subject of many experimental and theoretical studies (see [4] for a review). In this phase magnetic flux penetrates the superconductor by forming vortices, which are arranged in lattice geometries. Using several microscopic techniques, these periodic arrays of vortices have been experimentally studied in the lab both for conventional and for higher temperature superconductors. The Ginzburg-Landau (GL) theory is a very useful macroscopic description of superconductors (see [5] for a textbook) which can be used to model the Abrikosov vortex lattice
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