Abstract
We use holography to study the ground state of a system with interacting bosonic and fermionic degrees of freedom at finite density. The gravitational model consists of Einstein-Maxwell gravity coupled to a perfect fluid of charged fermions and to a charged scalar field which interact through a current-current interaction. When the scalar field is non-trivial, in addition to compact electron stars, the screening of the fermion electric charge by the scalar condensate allows the formation of solutions where the fermion fluid is made of antiparticles, as well as solutions with coexisting, separated regions of particle-like and antiparticle-like fermion fluids. We show that, when the latter solutions exist, they are thermodynamically favored. By computing the two-point Green function of the boundary fermionic operator we show that, in addition to the charged scalar condensate, the dual field theory state exhibits electron-like and/or hole-like Fermi surfaces. Compared to fluid-only solutions, the presence of the scalar condensate destroys the Fermi surfaces with lowest Fermi momenta. We interpret this as a signal of the onset of superconductivity.
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References
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].
J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].
S. Sachdev, Compressible quantum phases from conformal field theories in 2+1 dimensions, Phys. Rev. D 86 (2012) 126003 [arXiv:1209.1637] [INSPIRE].
S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].
S.A. Hartnoll and L. Huijse, Fractionalization of holographic Fermi surfaces, Class. Quant. Grav. 29 (2012) 194001 [arXiv:1111.2606] [INSPIRE].
A. Adam, B. Crampton, J. Sonner and B. Withers, Bosonic fractionalisation transitions, JHEP 01 (2013) 127 [arXiv:1208.3199] [INSPIRE].
B. Gouteraux and E. Kiritsis, Quantum critical lines in holographic phases with (un)broken symmetry, JHEP 04 (2013) 053 [arXiv:1212.2625] [INSPIRE].
P. Basu, J. He, A. Mukherjee, M. Rozali and H.-H. Shieh, Competing holographic orders, JHEP 10 (2010) 092 [arXiv:1007.3480] [INSPIRE].
A. Donos, J.P. Gauntlett, J. Sonner and B. Withers, Competing orders in M-theory: superfluids, stripes and metamagnetism, JHEP 03 (2013) 108 [arXiv:1212.0871] [INSPIRE].
D. Musso, Competition/enhancement of two probe order parameters in the unbalanced holographic superconductor, JHEP 06 (2013) 083 [arXiv:1302.7205] [INSPIRE].
R.-G. Cai, L. Li, L.-F. Li and Y.-Q. Wang, Competition and coexistence of order parameters in holographic multi-band superconductors, JHEP 09 (2013) 074 [arXiv:1307.2768] [INSPIRE].
Z.-Y. Nie, R.-G. Cai, X. Gao and H. Zeng, Competition between the s-wave and p-wave superconductivity phases in a holographic model, JHEP 11 (2013) 087 [arXiv:1309.2204] [INSPIRE].
I. Amado, D. Arean, A. Jimenez-Alba, L. Melgar and I. Salazar Landea, Holographic s + p superconductors, Phys. Rev. D 89 (2014) 026009 [arXiv:1309.5086] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Competing p-wave orders, Class. Quant. Grav. 31 (2014) 055007 [arXiv:1310.5741] [INSPIRE].
L.-F. Li, R.-G. Cai, L. Li and Y.-Q. Wang, Competition between s-wave order and d-wave order in holographic superconductors, JHEP 08 (2014) 164 [arXiv:1405.0382] [INSPIRE].
F. Nitti, G. Policastro and T. Vanel, Dressing the electron star in a holographic superconductor, JHEP 10 (2013) 019 [arXiv:1307.4558] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].
Y. Liu, K. Schalm, Y.-W. Sun and J. Zaanen, Bose-Fermi competition in holographic metals, JHEP 10 (2013) 064 [arXiv:1307.4572] [INSPIRE].
T. Hartman and S.A. Hartnoll, Cooper pairing near charged black holes, JHEP 06 (2010) 005 [arXiv:1003.1918] [INSPIRE].
Y. Liu, K. Schalm, Y.-W. Sun and J. Zaanen, BCS instabilities of electron stars to holographic superconductors, JHEP 05 (2014) 122 [arXiv:1404.0571] [INSPIRE].
S.A. Hartnoll, D.M. Hofman and D. Vegh, Stellar spectroscopy: fermions and holographic Lifshitz criticality, JHEP 08 (2011) 096 [arXiv:1105.3197] [INSPIRE].
M. Cubrovic, Y. Liu, K. Schalm, Y.-W. Sun and J. Zaanen, Spectral probes of the holographic Fermi groundstate: dialing between the electron star and AdS Dirac hair, Phys. Rev. D 84 (2011) 086002 [arXiv:1106.1798] [INSPIRE].
S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [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].
L.D. Landau and E.M. Lifshitz, Quantum mechanics: non-relativistic theory, Butterworth-Heinemann, U.K. (1981).
T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].
M. Oshikawa, Topological approach to Luttinger’s theorem and the Fermi surface of a Kondo lattice, Phys. Rev. Lett. 84 (2000) 3370 [cond-mat/0002392].
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Nitti, F., Policastro, G. & Vanel, T. Polarized solutions and Fermi surfaces in holographic Bose-Fermi systems. J. High Energ. Phys. 2014, 27 (2014). https://doi.org/10.1007/JHEP12(2014)027
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DOI: https://doi.org/10.1007/JHEP12(2014)027