Abstract
We present a minimal holographic model for s-wave superconductivity with unbalanced Fermi mixtures, in 2 + 1 dimensions at strong coupling. The breaking of a U(1) A “charge” symmetry is driven by a non-trivial profile for a charged scalar field in a charged asymptotically AdS 4 black hole. The chemical potential imbalance is implemented by turning on the temporal component of a U(1) B “spin” field under which the scalar field is uncharged. We study the phase diagram of the model and comment on the eventual (non) occurrence of LOFF-like inhomogeneous superconducting phases. Moreover, we study “charge” and “spin” transport, implementing a holographic realization (and a generalization thereof to superconducting setups) of Mott’s two-current model which provides the theoretical basis of modern spintronics. Finally we comment on possible string or M-theory embeddings of our model and its higher dimensional generalizations, within consistent Kaluza-Klein truncations and brane-anti brane setups.
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References
R. Casalbuoni and G. Nardulli, Inhomogeneous superconductivity in condensed matter and QCD, Rev. Mod. Phys. 76 (2004) 263 [hep-ph/0305069] [INSPIRE].
A. larkin and Y. Ovchinnikov, Nonuniform state of superconductors, Zh. Eksp. Teor. Fiz. 47 (1964) 1136 [INSPIRE].
P. Fulde and R.A. Ferrell, Superconductivity in a strong spin-exchange field, Phys. Rev. 135 (1964) A 550 [INSPIRE].
B.S. Chandrasekhar, A note on the maximum critical field of high field superconductors, Appl. Phys. Lett. 1 (1962) 7.
A.M. Clogston, Upper limit for the critical field in hard superconductors, Phys. Rev. Lett. 9 (1962) 266.
A. Fert, Nobel lecture: origin, development and future of spintronics, Rev. Mod. Phys. 80 (2008) 1517 [INSPIRE].
I. Zutic, J. Fabian and S. Das Sarma, Spintronics: fundamentals and applications, Rev. Mod. Phys. 76 (2004) 1323.
N.F. Mott, The electrical conductivity of transition metals, Proc. Roy. Soc. Lond. A 153 (1936) 699.
N.F. Mott, The resistance and thermoelectric properties of the transition metals, Proc. Roy. Soc. Lond. A 156 (1936) 368.
A. Fert and I.A. Campbell, Two-current conduction in nickel, Phys. Rev. Lett. 21 (1968) 1190.
P.C. van Son, H. van Kempen and P. Wyder, Boundary resistance of the ferromagnetic-nonferromagnetic metal interface, Phys. Rev. Lett. 58 (1987) 2271.
M. Johnson and R. H. Silsbee, Thermodynamic analysis of interfacial transport and of the thermomagnetoelectric system, Phys. Rev. B 35 (1987) 4959.
N. Iqbal, H. Liu, M. Mezei and Q. Si, Quantum phase transitions in holographic models of magnetism and superconductors, Phys. Rev. D 82 (2010) 045002 [arXiv:1003.0010] [INSPIRE].
K.W. Kim, J.W. Moon and K.J. Lee, Effect of spin diffusion on current generated by spin motive force, Phys. Rev. B 84 (2011) 054462.
J. Shibata and H. Kohno, Spin and charge transport induced by gauge fields in a ferromagnet, Phys. Rev. B 84 (2011) 184408 [arXiv:1107.2165].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
S.-J. Rey, String theory on thin semiconductors: holographic realization of Fermi points and surfaces, Prog. Theor. Phys. Suppl. 177 (2009) 128 [arXiv:0911.5295] [INSPIRE].
G.T. Horowitz, Introduction to holographic superconductors, arXiv:1002.1722 [INSPIRE].
S.A. Hartnoll, Horizons, holography and condensed matter, arXiv:1106.4324 [INSPIRE].
S. Sachdev, What can gauge-gravity duality teach us about condensed matter physics?, arXiv:1108.1197 [INSPIRE].
N. Iqbal, H. Liu and M. Mezei, Lectures on holographic non-Fermi liquids and quantum phase transitions, arXiv:1110.3814 [INSPIRE].
S. Sachdev, Condensed matter and AdS/CFT, arXiv:1002.2947 [INSPIRE].
S. Sachdev and B. Keimer, Quantum criticality, Phys. Today 64N2 (2011) 29 [arXiv:1102.4628].
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, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
J. Erdmenger, V. Grass, P. Kerner and T.H. Ngo, Holographic superfluidity in imbalanced Mixtures, JHEP 08 (2011) 037 [arXiv:1103.4145] [INSPIRE].
S.S. Gubser, Colorful horizons with charge in Anti-de Sitter space, Phys. Rev. Lett. 101 (2008) 191601 [arXiv:0803.3483] [INSPIRE].
S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic helical superconductors, JHEP 12 (2011) 091 [arXiv:1109.3866] [INSPIRE].
R. Combescot, Introduction to FFLO phases and collective mode in the BEC-BCS crossover, cond-mat/0702399.
R. Combescot and C. Mora, Transition to Fulde-Ferrel-Larkin-Ovchinnikov phases near the tricritical point: an analytical study, Eur. Phys. J. B 28 (2002) 397 [cond-mat/0203031].
M.G. Alford, K. Rajagopal and F. Wilczek, Color flavor locking and chiral symmetry breaking in high density QCD, Nucl. Phys. B 537 (1999) 443 [hep-ph/9804403] [INSPIRE].
K. Rajagopal and F. Wilczek, The condensed matter physics of QCD, in At the frontier of particle physics, volume 3, M. Shifman ed., World Scientific, Singapore (2001), hep-ph/0011333 [INSPIRE].
M.G. Alford, A. Schmitt, K. Rajagopal and T. Schafer, Color superconductivity in dense quark matter, Rev. Mod. Phys. 80 (2008) 1455 [arXiv:0709.4635] [INSPIRE].
M. Alford, J.A. Bowers and K. Rajagopal, Crystalline color superconductivity, Phys. Rev. D 63 (2001) 074016 [hep-ph/0008208] [INSPIRE].
S. Giorgini, L.P. Pitaevskii and S. Stringari, Theory of ultracold atomic Fermi gases, Rev. Mod. Phys. 80 (2008) 1215 [arXiv:0706.3360] [INSPIRE].
M.W. Zwierlein, A. Schirotzek, C.H. Schunck and W. Ketterle, Fermionic superfluidity with imbalanced spin populations, Science 311 (2006) 492 [INSPIRE].
P.F. Bedaque, H. Caldas and G. Rupak, Phase separation in asymmetrical fermion superfluids, Phys. Rev. Lett. 91 (2003) 247002 [cond-mat/0306694] [INSPIRE].
M. Mannarelli, G. Nardulli and M. Ruggieri, Evaluating the phase diagram of superconductors with asymmetric spin populations, Phys. Rev. A 74 (2006) 033606 [cond-mat/0604579] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].
D.B. Kaplan, J.-W. Lee, D.T. Son and M.A. Stephanov, Conformality lost, Phys. Rev. D 80 (2009) 125005 [arXiv:0905.4752] [INSPIRE].
K. Jensen, A. Karch, D.T. Son and E.G. Thompson, Holographic Berezinskii-Kosterlitz-Thouless transitions, Phys. Rev. Lett. 105 (2010) 041601 [arXiv:1002.3159] [INSPIRE].
E. Nakano and W.-Y. Wen, Critical magnetic field in a holographic superconductor, Phys. Rev. D 78 (2008) 046004 [arXiv:0804.3180] [INSPIRE].
S. Nakamura, H. Ooguri and C.-S. Park, Gravity dual of spatially modulated phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].
P. Basu, A. Mukherjee and H.-H. Shieh, Supercurrent: vector hair for an AdS black hole, Phys. Rev. D 79 (2009) 045010 [arXiv:0809.4494] [INSPIRE].
C. Herzog, P. Kovtun and D. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [INSPIRE].
D. Arean, P. Basu and C. Krishnan, The many phases of holographic superfluids, JHEP 10 (2010) 006 [arXiv:1006.5165] [INSPIRE].
D. Arean, M. Bertolini, C. Krishnan and T. Prochazka, Quantum critical superfluid flows and anisotropic domain walls, JHEP 09 (2011) 131 [arXiv:1106.1053] [INSPIRE].
C.P. Herzog, P. Kovtun, S. Sachdev and D.T. Son, Quantum critical transport, duality and M-theory, Phys. Rev. D 75 (2007) 085020 [hep-th/0701036] [INSPIRE].
B. Bellazzini, M. Burrello, M. Mintchev and P. Sorba, Quantum field theory on star graphs, Proc. Symp. Pure Math. 77 (2008) 639 [arXiv:0801.2852] [INSPIRE].
M. Nakajima et al., Evolution of the optical spectrum with doping in Ba(Fe 1−x Co x )2 As 2, Phys. Rev. B 81 (2010) 104528.
S. Takahashi and S. Maekawa, Spin injection and detection in magnetic nanostructures, Phys. Rev. B 67 (2003) 052409 [cond-mat/0212317].
F. Giazotto and F. Taddei, Superconductors as spin sources for spintronics, Phys. Rev. B 77 (2008) 132501 [arXiv:0711.0662].
S. Franco, A. Garcia-Garcia and D. Rodriguez-Gomez, A general class of holographic superconductors, JHEP 04 (2010) 092 [arXiv:0906.1214] [INSPIRE].
S. Franco, A.M. Garcia-Garcia and D. Rodriguez-Gomez, A holographic approach to phase transitions, Phys. Rev. D 81 (2010) 041901 [arXiv:0911.1354] [INSPIRE].
F. Aprile, S. Franco, D. Rodriguez-Gomez and J.G. Russo, Phenomenological models of holographic superconductors and Hall currents, JHEP 05 (2010) 102 [arXiv:1003.4487] [INSPIRE].
N.J. Evans and M. Petrini, Superfluidity in the AdS/CFT correspondence, JHEP 11 (2001) 043 [hep-th/0108052] [INSPIRE].
F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [INSPIRE].
J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [INSPIRE].
J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum criticality and holographic superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].
A. Donos, J.P. Gauntlett, N. Kim and O. Varela, Wrapped M5-branes, consistent truncations and AdS/CMT, JHEP 12 (2010) 003 [arXiv:1009.3805] [INSPIRE].
M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].
L. Romans, Gauged N = 4 supergravities in five-dimensions and their Magnetovac backgrounds, Nucl. Phys. B 267 (1986) 433 [INSPIRE].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [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].
F. Bigazzi, R. Casero, A. Cotrone, E. Kiritsis and A. Paredes, Non-critical holography and four-dimensional CFT’s with fundamentals, JHEP 10 (2005) 012 [hep-th/0505140] [INSPIRE].
R. Casero, E. Kiritsis and A. Paredes, Chiral symmetry breaking as open string tachyon condensation, Nucl. Phys. B 787 (2007) 98 [hep-th/0702155] [INSPIRE].
S. Sugimoto and K. Takahashi, QED and string theory, JHEP 04 (2004) 051 [hep-th/0403247] [INSPIRE].
R. Casero, A. Paredes and J. Sonnenschein, Fundamental matter, meson spectroscopy and non-critical string/gauge duality, JHEP 01 (2006) 127 [hep-th/0510110] [INSPIRE].
G. Bertoldi, F. Bigazzi, A. Cotrone and J.D. Edelstein, Holography and unquenched quark-gluon plasmas, Phys. Rev. D 76 (2007) 065007 [hep-th/0702225] [INSPIRE].
A. Sen, Dirac-Born-Infeld action on the tachyon kink and vortex, Phys. Rev. D 68 (2003) 066008 [hep-th/0303057] [INSPIRE].
M.R. Garousi, D-brane D-brane effective action and brane interaction in open string channel, JHEP 01 (2005) 029 [hep-th/0411222] [INSPIRE].
M.R. Garousi, On the effective action of D-brane- D-brane system, JHEP 12 (2007) 089 [arXiv:0710.5469] [INSPIRE].
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Bigazzi, F., Cotrone, A.L., Musso, D. et al. Unbalanced holographic superconductors and spintronics. J. High Energ. Phys. 2012, 78 (2012). https://doi.org/10.1007/JHEP02(2012)078
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DOI: https://doi.org/10.1007/JHEP02(2012)078