Abstract
We study the magnetic response of holographic superconductors exhibiting an insulating ‘normal’ phase. These materials can be realized as a CFT compactified on a circle, which is dual to the AdS Soliton geometry. We study the response under i) magnetic fields and ii) a Wilson line on the circle. Magnetic fields lead to formation of vortices and allows one to infer that the superconductor is of type II. The response to a Wilson line is in the form of Aharonov-Bohm-like effects. These are suppressed in the holographic conductor/superconductor transition but, instead, they are unsuppressed for the insulator case. Holography, thus, predicts that generically insulators display stronger Aharonov-Bohm effects than conductors. In the fluid-mechanical limit the AdS Soliton is interpreted as a supersolid. Our results imply that supersolids display unsuppressed Aharonov-Bohm (or ‘Sagnac’) effects — stronger than in superfluids.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
P.A. Lee, N. Nagaosa and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78 (2006) 17 [INSPIRE].
T. Nishioka, S. Ryu and T. Takayanagi, Holographic Superconductor/Insulator Transition at Zero Temperature, JHEP 03 (2010) 131 [arXiv:0911.0962] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
G.T. Horowitz and R.C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev. D 59 (1998) 026005 [hep-th/9808079] [INSPIRE].
V. Juričić, I.F. Herbut and Z. Tesanović, Restoration of the Magnetic hc/e-Periodicity in Unconventional Superconductors, Phys. Rev. Lett. 100 (2008) 187006.
V. Vakaryuk, Universal Mechanism for Breaking the hc/2e Periodicity of Flux-Induced Oscillations in Small Superconducting Rings, Phys. Rev. Lett. 101 (2008) 167002.
F. Loder et al., Magnetic flux periodicity of h/e in superconducting loops, Nat. Phys. 4 (2008) 112.
T.C. Wei and P.M. Goldbart, Emergence of h/e-period oscillations in the critical temperature of small superconducting rings threaded by magnetic flux, Phys. Rev. B 77 (2008) 224512.
Y.S. Barash, Low-Energy Subgap States and the Magnetic Flux Periodicity in d-Wave Superconducting Rings, Phys. Rev. Lett. 100 (2008) 177003.
M. Buttiker, Y. Imry and R. Landauer, Josephson Behavior in Small Normal One-Dimensional Rings, Phys. Lett. A 96 (1983) 365.
R. Landauer and M. Buttiker, Resistance of Small Metallic Loops, Phys. Rev. Lett. 54 (1985) 18.
L. Levy, G. Dolan, J. Dunsmuir and H. Bouchiat, Magnetization of mesoscopic copper rings: Evidence for persistent currents, Phys. Rev. Lett. 64 (1990) 2074 [INSPIRE].
V. Chandrasekhar, R.A. Webb , M. Brady, M.B. Ketchen, W.J. Gallagher and A. Kelinsasser, Magnetic Response of a Single, Isolated Gold Loop, Phys. Rev. Lett. 67 (1991) 3578.
D. Mailly, C. Chapelier and A. Benoit, Experimental Observation of Persistent Currents in a GaAs-AlGaAs Single Loop, Phys. Rev. Lett. 70 (1993) 2020.
H. Bluhm, N.C. Koshnick, J.A. Bert, M.E. Huber and K.A. Moler, Persistent Currents in Normal Metal Rings, Phys. Rev. Lett. 102 (2009) 136802.
R.A. Webb, S. Washburn, C.P. Umbach and R.B. Laibowitz, Observation of h/e Aharonov-Bohm Oscillations in Normal-Metal Rings, Phys. Rev. Lett. 54 (1985) 2696.
M. Montull, O. Pujolàs, A. Salvio and P.J. Silva, Flux Periodicities and Quantum Hair on Holographic Superconductors, Phys. Rev. Lett. 107 (2011) 181601 [arXiv:1105.5392] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
T. Albash and C.V. Johnson, A Holographic Superconductor in an External Magnetic Field, JHEP 09 (2008) 121 [arXiv:0804.3466] [INSPIRE].
E. Nakano and W.-Y. Wen, Critical magnetic field in a holographic superconductor, Phys. Rev. D 78 (2008) 046004 [arXiv:0804.3180] [INSPIRE].
K. Maeda and T. Okamura, Characteristic length of an AdS/CFT superconductor, Phys. Rev. D 78 (2008) 106006 [arXiv:0809.3079] [INSPIRE].
X.-H. Ge, B. Wang, S.-F. Wu and G.-H. Yang, Analytical study on holographic superconductors in external magnetic field, JHEP 08 (2010) 108 [arXiv:1002.4901] [INSPIRE].
T. Albash and C.V. Johnson, Phases of Holographic Superconductors in an External Magnetic Field, arXiv:0906.0519 [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. 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, JHEP 08 (2010) 033 [arXiv:1005.1776] [INSPIRE].
S. Weinberg, Superconductivity for particular theorists, Prog. Theor. Phys. Suppl. 86 (1986) 43 [INSPIRE].
Y. Hosotani, Dynamics of Nonintegrable Phases and Gauge Symmetry Breaking, Annals Phys. 190 (1989) 233 [INSPIRE].
G. Dvali, Black holes with quantum massive spin-2 hair, Phys. Rev. D 74 (2006) 044013 [hep-th/0605295] [INSPIRE].
A.F. Andreev and I.M. Lifshitz, Quantum theory of Crystal Defects, Sov. Phys. JETP 29 (1969) 1107.
E. Kim and M.H.W. Chan, Probable observation of a supersolid helium phase, Nature 427 (2004) 225.
E. Kim and M.H.W. Chan, Observation of Superflow in Solid Helium, Science 305 (2004) 1941.
D. Son, Effective Lagrangian and topological interactions in supersolids, Phys. Rev. Lett. 94 (2005) 175301 [cond-mat/0501658] [INSPIRE].
G. During, C. Josserand, Y. Pomeau and S. Rica, Theory of real supersolids, arXiv:1110.1323.
HPQCD collaboration, A. Gray et al., The B meson decay constant from unquenched lattice QCD, Phys. Rev. Lett. 95 (2005) 212001 [hep-lat/0507015] [INSPIRE].
J. Anandan, Gravitational and Inertial Effects in Quantum Fluids, Phys. Rev. Lett. 47 (1981) 7.
Y. Sato and R. E. Packard, Superfluid helium quantum interference devices: physics and applications, Rep. Prog. Phys. 75 (2012) 016401.
G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].
N. Arkani-Hamed, M. Porrati and L. Randall, Holography and phenomenology, JHEP 08 (2001) 017 [hep-th/0012148] [INSPIRE].
L.G. Yaffe, Large-N Limits as Classical Mechanics, Rev. Mod. Phys. 54 (1982) 407 [INSPIRE].
E. Witten, Theta dependence in the large-N limit of four-dimensional gauge theories, Phys. Rev. Lett. 81 (1998) 2862 [hep-th/9807109] [INSPIRE].
R.-G. Cai, L. Li, H.-Q. Zhang and Y.-L. Zhang, Magnetic Field Effect on the Phase Transition in AdS Soliton Spacetime, Phys. Rev. D 84 (2011) 126008 [arXiv:1109.5885] [INSPIRE].
W.H. Kleiner, L.M. Roth and S.H. Autler, Bulk Solution of Ginzburg-Landau Equations for Type II Superconductors: Upper Critical Field Region, Phys. Rev. A 133 (1964) 1226.
K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev. D 81 (2010) 026002 [arXiv:0910.4475] [INSPIRE].
G.T. Horowitz and B. Way, Complete Phase Diagrams for a Holographic Superconductor/Insulator System, JHEP 11 (2010) 011 [arXiv:1007.3714] [INSPIRE].
Y. Brihaye and B. Hartmann, Holographic superfluid/fluid/insulator phase transitions in 2+1 dimensions, Phys. Rev. D 83 (2011) 126008 [arXiv:1101.5708] [INSPIRE].
G.T. Horowitz, J.E. Santos and B. Way, A Holographic Josephson Junction, Phys. Rev. Lett. 106 (2011) 221601 [arXiv:1101.3326] [INSPIRE].
S.S. Gubser and S.S. Pufu, The Gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [INSPIRE].
M.M. Roberts and S.A. Hartnoll, Pseudogap and time reversal breaking in a holographic superconductor, JHEP 08 (2008) 035 [arXiv:0805.3898] [INSPIRE].
M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Superconductivity from gauge/gravity duality with flavor, Phys. Lett. B 680 (2009) 516 [arXiv:0810.2316] [INSPIRE].
M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Flavor Superconductivity from Gauge/Gravity Duality, JHEP 10 (2009) 067 [arXiv:0903.1864] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1202.0006
Rights and permissions
About this article
Cite this article
Montull, M., Pujolàs, O., Salvio, A. et al. Magnetic response in the holographic insulator/superconductor transition. J. High Energ. Phys. 2012, 135 (2012). https://doi.org/10.1007/JHEP04(2012)135
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2012)135