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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Sachdev, Quantum phase transitions, 1st edition, Cambridge University Press, Cambridge, U.K. (1999).
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
A.A. Abrikosov, On the magnetic properties of superconductors of the second group, Sov. Phys. JETP5 (1957) 1174 [Zh. Eksp. Teor. Fiz.32 (1957) 1442] [INSPIRE].
E.H. Brandt, The flux-line lattice in superconductors, Rep. Prog. Phys.58 (1995) 1465.
M. Tinkham, Introduction to superconductivity, 2nd edition, Dover publications, Mineola, NY, U.S.A. (1996).
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev.D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett.101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
J. Zaanen, Y. Liu, Y.-W. Sun and K. Schalm, Holographic duality in condensed matter physics, Cambridge University Press, Cambridge, U.K. (2015) [INSPIRE].
T. Albash and C.V. Johnson, Vortex and droplet engineering in holographic superconductors, Phys. Rev.D 80 (2009) 126009 [arXiv:0906.1795] [INSPIRE].
M. Montull, A. Pomarol and P.J. Silva, The holographic superconductor vortex, Phys. Rev. Lett.103 (2009) 091601 [arXiv:0906.2396] [INSPIRE].
V. Keranen, E. Keski-Vakkuri, S. Nowling and K.P. Yogendran, Inhomogeneous structures in holographic superfluids: II. Vortices, Phys. Rev.D 81 (2010) 126012 [arXiv:0912.4280] [INSPIRE].
O. Domenech, M. Montull, A. Pomarol, A. Salvio and P.J. Silva, Emergent gauge fields in holographic superconductors, JHEP08 (2010) 033 [arXiv:1005.1776] [INSPIRE].
G. Tallarita and S. Thomas, Maxwell-Chern-Simons vortices and holographic superconductors, JHEP12 (2010) 090 [arXiv:1007.4163] [INSPIRE].
N. Iqbal and H. Liu, Luttinger’s theorem, superfluid vortices and holography, Class. Quant. Grav.29 (2012) 194004 [arXiv:1112.3671] [INSPIRE].
G. Tallarita, Non-Abelian vortices in holographic superconductors, Phys. Rev.D 93 (2016) 066011 [arXiv:1510.06719] [INSPIRE].
Ó.J.C. Dias, G.T. Horowitz, N. Iqbal and J.E. Santos, Vortices in holographic superfluids and superconductors as conformal defects, JHEP04 (2014) 096 [arXiv:1311.3673] [INSPIRE].
K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev.D 81 (2010) 026002 [arXiv:0910.4475] [INSPIRE].
N. Bao, S. Harrison, S. Kachru and S. Sachdev, Vortex lattices and crystalline geometries, Phys. Rev.D 88 (2013) 026002 [arXiv:1303.4390] [INSPIRE].
N. Bao and S. Harrison, Crystalline scaling geometries from vortex lattices, Phys. Rev.D 88 (2013) 046009 [arXiv:1306.1532] [INSPIRE].
Y.-Y. Bu, J. Erdmenger, J.P. Shock and M. Strydom, Magnetic field induced lattice ground states from holography, JHEP03 (2013) 165 [arXiv:1210.6669] [INSPIRE].
C.-Y. Xia, H.-B. Zeng, H.-Q. Zhang, Z.-Y. Nie, Y. Tian and X. Li, Vortex lattice in a rotating holographic superfluid, Phys. Rev.D 100 (2019) 061901 [arXiv:1904.10925] [INSPIRE].
X. Li, Y. Tian and H. Zhang, Generation of vortices and stabilization of vortex lattices in holographic superfluids, arXiv:1904.05497 [INSPIRE].
D. Ihle, Wigner-Seitz approximation for the description of the mixed state of type II superconductors, Phys. Stat. Sol.B 47 (1971) 423.
W.V. Pogosov, K.I. Kugel, A.L. Rakhmanov and E.H. Brandt, Approximate Ginzburg-Landau solution for the regular flux-line lattice: circular cell method, Phys. Rev.B 64 (2001) 064517 [cond-mat/0011057].
E.H. Brandt, Properties of the ideal Ginzburg-Landau vortex lattice, Phys. Rev.B 68 (2003) 054506 [cond-mat/0304237].
E.H. Brandt, Some properties of the ideal Ginzburg-Landau vortex lattice, PhysicaC 404 (2004) 74.
T. Faulkner, G.T. Horowitz and M.M. Roberts, Holographic quantum criticality from multi-trace deformations, JHEP04 (2011) 051 [arXiv:1008.1581] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
M. Berkooz, A. Sever and A. Shomer, ‘Double trace’ deformations, boundary conditions and space-time singularities, JHEP05 (2002) 034 [hep-th/0112264] [INSPIRE].
S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev.D 76 (2007) 066001 [arXiv:0704.1160] [INSPIRE].
S.A. Hartnoll, P.K. Kovtun, M. Muller and S. Sachdev, Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes, Phys. Rev.B 76 (2007) 144502 [arXiv:0706.3215] [INSPIRE].
M. Ammon and J. Erdmenger, Gauge/gravity duality: foundations and applications, Cambridge University Press, Cambridge, U.K. (2015) [INSPIRE].
E. Witten, SL(2, Z) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Numerical methods for finding stationary gravitational solutions, Class. Quant. Grav.33 (2016) 133001 [arXiv:1510.02804] [INSPIRE].
G. Tallarita, R. Auzzi and A. Peterson, The holographic non-Abelian vortex, JHEP03 (2019) 114 [arXiv:1901.05814] [INSPIRE].
A. Hanany and D. Tong, Vortices, instantons and branes, JHEP07 (2003) 037 [hep-th/0306150] [INSPIRE].
R. Auzzi, S. Bolognesi, J. Evslin, K. Konishi and A. Yung, Non-Abelian superconductors: vortices and confinement in N = 2 SQCD, Nucl. Phys.B 673 (2003) 187 [hep-th/0307287] [INSPIRE].
M. Shifman and A. Yung, Non-Abelian string junctions as confined monopoles, Phys. Rev.D 70 (2004) 045004 [hep-th/0403149] [INSPIRE].
M. Shifman, Simple models with non-Abelian moduli on topological defects, Phys. Rev.D 87 (2013) 025025 [arXiv:1212.4823] [INSPIRE].
K. Hashimoto and D. Tong, Reconnection of non-Abelian cosmic strings, JCAP09 (2005) 004 [hep-th/0506022] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Moduli space of non-Abelian vortices, Phys. Rev. Lett.96 (2006) 161601 [hep-th/0511088] [INSPIRE].
R. Auzzi, M. Shifman and A. Yung, Composite non-Abelian flux tubes in N = 2 SQCD, Phys. Rev.D 73 (2006) 105012 [Erratum ibid.D 76 (2007) 109901] [hep-th/0511150] [INSPIRE].
R. Auzzi, M. Eto and W. Vinci, Type I non-Abelian superconductors in supersymmetric gauge theories, JHEP11 (2007) 090 [arXiv:0709.1910] [INSPIRE].
R. Auzzi, M. Eto and W. Vinci, Static interactions of non-Abelian vortices, JHEP02 (2008) 100 [arXiv:0711.0116] [INSPIRE].
G. Tallarita and A. Peterson, Non-Abelian vortex lattices, Phys. Rev.D 97 (2018) 076003 [arXiv:1710.07806] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1909.05932
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Tallarita, G., Auzzi, R. The holographic vortex lattice using the circular cell method. J. High Energ. Phys. 2020, 56 (2020). https://doi.org/10.1007/JHEP01(2020)056
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2020)056