Holographic Abrikosov lattices

Abstract

We study black hole solutions of D = 4 Einstein-Maxwell theory coupled to a charged scalar field that are holographically dual to a d = 3 conformal field theory with a non-vanishing chemical potential and constant magnetic field. We numerically construct black hole solutions that are dual to a superfluid phase with a periodic lattice of vortices. For the specific model we investigate, we find that the thermodynamically preferred con- figuration is given by a triangular lattice and moreover the vortices are associated with the lowest Landau level. We also construct black holes describing a lattice of vortices associated with the next to lowest Landau level and while these are not thermodynamically preferred they exhibit some interesting features that could be realised for other holographic models.

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References

  1. [1]

    S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].

  2. [2]

    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett.101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].

  3. [3]

    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP12 (2008) 015 [arXiv:0810.1563] [INSPIRE].

  4. [4]

    M. Ammon, J. Erdmenger, P. Kerner and M. Strydom, Black hole instability induced by a magnetic field, Phys. Lett. B706 (2011) 94 [arXiv:1106.4551] [INSPIRE].

  5. [5]

    E. Nakano and W.-Y. Wen, Critical magnetic field in a holographic superconductor, Phys. Rev. D78 (2008) 046004 [arXiv:0804.3180] [INSPIRE].

  6. [6]

    T. Albash and C.V. Johnson, A holographic superconductor in an external magnetic field, JHEP09 (2008) 121 [arXiv:0804.3466] [INSPIRE].

  7. [7]

    T. Albash and C.V. Johnson, Phases of holographic superconductors in an external magnetic field, arXiv:0906.0519 [INSPIRE].

  8. [8]

    T. Albash and C.V. Johnson, Vortex and droplet engineering in holographic superconductors, Phys. Rev. D80 (2009) 126009 [arXiv:0906.1795] [INSPIRE].

  9. [9]

    M. Montull, A. Pomarol and P.J. Silva, The holographic superconductor vortex, Phys. Rev. Lett.103 (2009) 091601 [arXiv:0906.2396] [INSPIRE].

  10. [10]

    C.-Y. Xia et al., Vortex lattice in a rotating holographic superfluid, Phys. Rev. D100 (2019) 061901 [arXiv:1904.10925] [INSPIRE].

  11. [11]

    W.-C. Yang, C.-Y. Xia, H.-B. Zeng and H.-Q. Zhang, Phase separation and exotic vortex phases in a two-species holographic superfluid, arXiv:1907.01918 [INSPIRE].

  12. [12]

    K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev. D81 (2010) 026002 [arXiv:0910.4475] [INSPIRE].

  13. [13]

    N. Bao, S. Harrison, S. Kachru and S. Sachdev, Vortex lattices and crystalline geometries, Phys. Rev. D88 (2013) 026002 [arXiv:1303.4390] [INSPIRE].

  14. [14]

    G. Tallarita and R. Auzzi, The holographic vortex lattice using the circular cell method, JHEP01 (2020) 056 [arXiv:1909.05932] [INSPIRE].

  15. [15]

    B. Rosenstein and D. Li, Ginzburg-Landau theory of type II superconductors in magnetic field, Rev. Mod. Phys.82 (2010) 109.

  16. [16]

    E. Banks and J.P. Gauntlett, A new phase for the anisotropic N = 4 super Yang-Mills plasma, JHEP09 (2015) 126 [arXiv:1506.07176] [INSPIRE].

  17. [17]

    A. Donos and J.P. Gauntlett, Helical superconducting black holes, Phys. Rev. Lett.108 (2012) 211601 [arXiv:1203.0533] [INSPIRE].

  18. [18]

    A. Donos and J.P. Gauntlett, Black holes dual to helical current phases, Phys. Rev. D86 (2012) 064010 [arXiv:1204.1734] [INSPIRE].

  19. [19]

    A. Donos, Striped phases from holography, JHEP05 (2013) 059 [arXiv:1303.7211] [INSPIRE].

  20. [20]

    B. Withers, Black branes dual to striped phases, Class. Quant. Grav.30 (2013) 155025 [arXiv:1304.0129] [INSPIRE].

  21. [21]

    B. Withers, The moduli space of striped black branes, arXiv:1304.2011 [INSPIRE].

  22. [22]

    M. Rozali, D. Smyth, E. Sorkin and J.B. Stang, Striped order in AdS/CFT correspondence, Phys. Rev. D87 (2013) 126007 [arXiv:1304.3130] [INSPIRE].

  23. [23]

    A. Donos, J.P. Gauntlett and C. Pantelidou, Competing p-wave orders, Class. Quant. Grav.31 (2014) 055007 [arXiv:1310.5741] [INSPIRE].

  24. [24]

    B. Withers, Holographic checkerboards, JHEP09 (2014) 102 [arXiv:1407.1085] [INSPIRE].

  25. [25]

    A. Donos and J.P. Gauntlett, Minimally packed phases in holography, JHEP03 (2016) 148 [arXiv:1512.06861] [INSPIRE].

  26. [26]

    A. Donos and C. Pantelidou, Holographic magnetisation density waves, JHEP10 (2016) 038 [arXiv:1607.01807] [INSPIRE].

  27. [27]

    F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D79 (2009) 126008 [arXiv:0901.1160] [INSPIRE].

  28. [28]

    M. Headrick, S. Kitchen and T. Wiseman, A new approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav.27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].

  29. [29]

    P. Figueras, J. Lucietti and T. Wiseman, Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua, Class. Quant. Grav.28 (2011) 215018 [arXiv:1104.4489] [INSPIRE].

  30. [30]

    A. Donos and J.P. Gauntlett, On the thermodynamics of periodic AdS black branes, JHEP10 (2013) 038 [arXiv:1306.4937] [INSPIRE].

  31. [31]

    A. Donos, J.P. Gauntlett, T. Griffin and V. Ziogas, Incoherent transport for phases that spontaneously break translations, JHEP04 (2018) 053 [arXiv:1801.09084] [INSPIRE].

  32. [32]

    A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP04 (2014) 040 [arXiv:1311.3292] [INSPIRE].

  33. [33]

    M. Blake and A. Donos, Diffusion and chaos from near AdS2horizons, JHEP02 (2017) 013 [arXiv:1611.09380] [INSPIRE].

  34. [34]

    A. Donos, J.P. Gauntlett, C. Rosen and O. Sosa-Rodriguez, Boomerang RG flows with intermediate conformal invariance, JHEP04 (2018) 017 [arXiv:1712.08017] [INSPIRE].

  35. [35]

    O.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].

  36. [36]

    J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum criticality and holographic superconductors in M-theory, JHEP02 (2010) 060 [arXiv:0912.0512] [INSPIRE].

  37. [37]

    A. Donos, J.P. Gauntlett, J. Sonner and B. Withers, Competing orders in M-theory: superfluids, stripes and metamagnetism, JHEP03 (2013) 108 [arXiv:1212.0871] [INSPIRE].

  38. [38]

    P.A. Horvathy and P. Zhang, Vortices in (abelian) Chern-Simons gauge theory, Phys. Rept.481 (2009) 83 [arXiv:0811.2094] [INSPIRE].

  39. [39]

    G. Tallarita and S. Thomas, Maxwell-Chern-Simons vortices and holographic superconductors, JHEP12 (2010) 090 [arXiv:1007.4163] [INSPIRE].

  40. [40]

    A. Almheiri and J. Polchinski, Models of AdS2backreaction and holography, JHEP11 (2015) 014 [arXiv:1402.6334] [INSPIRE].

  41. [41]

    A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and electric AdS solutions in string- and M-theory, Class. Quant. Grav.29 (2012) 194006 [arXiv:1112.4195] [INSPIRE].

  42. [42]

    A. Donos and J.P. Gauntlett, The thermoelectric properties of inhomogeneous holographic lattices, JHEP01 (2015) 035 [arXiv:1409.6875] [INSPIRE].

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Correspondence to Jerome P. Gauntlett.

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Dedicated to the memory of Steven Gubser

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Donos, A., Gauntlett, J.P. & Pantelidou, C. Holographic Abrikosov lattices. J. High Energ. Phys. 2020, 95 (2020). https://doi.org/10.1007/JHEP07(2020)095

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Keywords

  • AdS-CFT Correspondence
  • Holography and condensed matter physics (AdS/CMT)