Abstract
The possibility of inter-layer exciton condensation in a holographic D3-probe-D5 brane model of a strongly coupled double monolayer Dirac semi-metal in a magnetic field is studied in detail. It is found that, when the charge densities on the layers are exactly balanced so that, at weak coupling, the Fermi surfaces of electrons in one monolayer and holes in the other monolayer would be perfectly nested, inter-layer condensates can form for any separation of the layers. The case where both monolayers are charge neutral is special. There, the inter-layer condensate occurs only for small separations and is replaced by an intra-layer exciton condensate at larger separations. The phase diagram for charge balanced monolayers for a range layer separations and chemical potentials is found. We also show that, in semi-metals with multiple species of massless fermions, the balance of charges required for Fermi surface nesting can occur spontaneously by breaking some of the internal symmetry of the monolayers. This could have important consequences for experimental attempts to find inter-layer condensates.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C.-H. Zhang and Y.N. Joglekar, Excitonic condensation of massless fermions in graphene bilayers, Phys. Rev. B 77 (2008) 233405 [arXiv:0803.3451].
Yu. E. Lozovik and A.A. Sokolik, Electron-hole pair condensation in a graphene bilayer, Pis’ma v ZhETF 87 (2008) 61 [JETP Lett. 87 2008 55] [arXiv:0812.4840].
B. Seradjeh, H. Weber and M. Franz, Vortices, zero modes, and fractionalization in the bilayer-graphene exciton condensate, Phys. Rev. Lett. 101 (2008) 246404 [arXiv:0806.0849].
H. Min, R. Bistritzer, J.-J. Su and A.H. MacDonald, Room-temperature superfluidity in graphene bilayers, Phys. Rev. B 78 (2008) 121401 [arXiv:0802.3462].
B. Seradjeh, J.E. Moore and M. Franz, Exciton condensation and charge fractionalization in a topological insulator film, Phys. Rev. Lett. 103 (2009) 066402 [arXiv:0902.1147].
D.S.L. Abergel, M. Rodriguez-Vega, E. Rossi and S. Das Sarma, Interlayer excitonic superfluidity in graphene, Phys. Rev. B 88 (2013) 235402 [arXiv:1305.4936].
A. Gamucci et al., Electron-hole pairing in graphene-GaAs heterostructures, arXiv:1401.0902 [INSPIRE].
A.A. High et al., Spontaneous coherence in a cold exciton gas, Nature 483 (2012) 584 [arXiv:1109.0253].
A.A. High et al., Spontaneous coherence of indirect excitons in a trap, Nano Lett. 12 (2012) 2605 [arXiv:1110.1337].
S. Utsunomiya et al., Observation of Bogoliubov excitations in exciton-polariton condensates, Nat. Phys. 4 (2008) 700.
K.G. Lagoudakis et al., Quantized vortices in an exciton-polariton condensate, Nat. Phys. 4 (2008) 706 [arXiv:0801.1916].
D. Nandi, A.D.K. Finck, J.P. Eisenstein, L.N. Pfeiffer and K.W. West, Exciton condensation and perfect Coulomb drag, Nature 488 (2012) 481 [arXiv:1203.3208].
S. Banerjee, L. Register, E. Tutuc, D. Reddy and A. MacDonald, Bilayer pseudospin field-effect transistor (BiSFET), a proposed new logic device, IEEE Electron Dev. Lett. 30 (2009) 158.
A.A. High, E.E. Novitskaya, L.V. Butov and A.C. Gossard, Control of exciton fluxes in an excitonic integrated circuit, Science 321 (2008) 229.
Y.Y. Kuznetsova et al., All-optical excitonic transistor, Opt. Lett. 35 (2010) 1587.
D. Ballarini et al., All-optical polariton transistor, Nat. Comm. 4 (2013) 1778 [arXiv:1201.4071].
F. Dolcini et al., Blockade and counterflow supercurrent in exciton-condensate Josephson junctions, Phys. Rev. Lett. 104 (2010) 027004 [arXiv:0908.0478].
S. Peotta et al., Josephson current in a four-terminal superconductor/exciton-condensate/superconductor system, Phys. Rev. B 84 (2011) 184528 [arXiv:1108.1533].
R.V. Gorbachev et al., Strong Coulomb drag and broken symmetry in double-layer graphene, Nat. Phys. 8 (2012) 896 [arXiv:1206.6626].
S. Kim et al., Coulomb drag of massless fermions in graphene, Phys. Rev. B 83 (2011) 161401(R) [arXiv:1010.2113].
D. Neilson, A. Perali and A.R. Hamilton, Excitonic superfluidity and screening in electron-hole bilayer systems, Phys. Rev. B 89 (2014) 060502(R) [arXiv:1308.0280].
Z.F. Ezawa and K. Hasebe, Interlayer exchange interactions, SU(4) soft waves, and skyrmions in bilayer quantum Hall ferromagnets, Phys. Rev. B 65 (2002) 075311 [cond-mat/0104448] [INSPIRE].
S.Q. Murphy, J.P. Eisenstein, G.S. Boebinger, L.W. Pfeiffer and K.W. West, Many-body integer quantum Hall effect: evidence for new phase transitions, Phys. Rev. Lett. 72 (1994) 728.
K. Moon et al., Spontaneous interlayer coherence in double-layer quantum Hall systems: charged vortices and Kosterlitz-Thouless phase transitions, Phys. Rev. B 51 (1995) 5138 [cond-mat/9407031].
Y. Zhang et al., Landau-level splitting in graphene in high magnetic fields, Phys. Rev. Lett. 96 (2006) 136806 [cond-mat/0602649].
A.F. Young et al., Spin and valley quantum Hall ferromagnetism in graphene, Nat. Phys. 8 (2012) 550 [arXiv:1201.4167].
D.A. Abanin et al., Dissipative quantum Hall effect in graphene near the Dirac point, Phys. Rev. Lett. 98 (2007) 196806 [cond-mat/0702125].
J.G. Checkelsky, L. Li and N.P. Ong, The zero-energy state in graphene in a high magnetic field, Phys. Rev. Lett. 100 (2008) 206801 [arXiv:0708.1959].
J.G. Checkelsky, L. Li and N.P. Ong, Divergent resistance at the Dirac point in graphene: evidence for a transition in a high magnetic field, Phys. Rev. B 79 (2009) 115434 [arXiv:0808.0906].
H.A. Fertig, Energy spectrum of a layered system in a strong magnetic field, Phys. Rev. B 40 (1989) 1087.
T. Jungwirth and A.H. MacDonald, Pseudospin anisotropy classification of quantum Hall ferromagnets, Phys. Rev. B 63 (2000) 035305 [cond-mat/0003430].
D.V. Khveshchenko, Magnetic field-induced insulating behavior in highly oriented pyrolitic graphite, Phys. Rev. Lett. 87 (2001) 206401 [cond-mat/0106261] [INSPIRE].
K. Nomura and A.H. MacDonald, Quantum Hall ferromagnetism in graphene, Phys. Rev. Lett. 96 (2006) 256602.
M.O. Goerbig, Electronic properties of graphene in a strong magnetic field, Rev. Mod. Phys. 83 (2011) 1193 [arXiv:1004.3396].
Y. Barlas, K. Yang and A. Macdonald, Quantum Hall effects in graphene-based two-dimensional electron systems, Nanotechnology 23 (2012) 052001 [arXiv:1110.1069].
K.G. Klimenko, Three-dimensional Gross-Neveu model in an external magnetic field, Theor. Math. Phys. 89 (1992) 1161 [INSPIRE].
V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Catalysis of dynamical flavor symmetry breaking by a magnetic field in (2+1)-dimensions, Phys. Rev. Lett. 73 (1994) 3499 [Erratum ibid. 76 (1996) 1005] [hep-ph/9405262] [INSPIRE].
V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Dynamical flavor symmetry breaking by a magnetic field in (2+1)-dimensions, Phys. Rev. D 52 (1995) 4718 [hep-th/9407168] [INSPIRE].
G.W. Semenoff, I.A. Shovkovy and L.C.R. Wijewardhana, Phase transition induced by a magnetic field, Mod. Phys. Lett. A 13 (1998) 1143 [hep-ph/9803371] [INSPIRE].
G.W. Semenoff, I.A. Shovkovy and L.C.R. Wijewardhana, Universality and the magnetic catalysis of chiral symmetry breaking, Phys. Rev. D 60 (1999) 105024 [hep-th/9905116] [INSPIRE].
V.G. Filev, C.V. Johnson and J.P. Shock, Universal holographic chiral dynamics in an external magnetic field, JHEP 08 (2009) 013 [arXiv:0903.5345] [INSPIRE].
G.W. Semenoff and F. Zhou, Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene, JHEP 07 (2011) 037 [arXiv:1104.4714] [INSPIRE].
S. Bolognesi and D. Tong, Magnetic catalysis in AdS 4, Class. Quant. Grav. 29 (2012) 194003 [arXiv:1110.5902] [INSPIRE].
J. Erdmenger, V.G. Filev and D. Zoakos, Magnetic catalysis with massive dynamical flavours, JHEP 08 (2012) 004 [arXiv:1112.4807] [INSPIRE].
S. Bolognesi, J.N. Laia, D. Tong and K. Wong, A gapless hard wall: magnetic catalysis in bulk and boundary, JHEP 07 (2012) 162 [arXiv:1204.6029] [INSPIRE].
I.A. Shovkovy, Magnetic catalysis: a review, Lect. Notes Phys. 871 (2013) 13 [arXiv:1207.5081] [INSPIRE].
M. Blake, S. Bolognesi, D. Tong and K. Wong, Holographic dual of the lowest Landau level, JHEP 12 (2012) 039 [arXiv:1208.5771] [INSPIRE].
V.G. Filev and M. Ihl, Flavoured large-N gauge theory on a compact space with an external magnetic field, JHEP 01 (2013) 130 [arXiv:1211.1164] [INSPIRE].
C. Kristjansen and G.W. Semenoff, Giant D5 brane holographic Hall state, JHEP 06 (2013) 048 [arXiv:1212.5609] [INSPIRE].
C. Kristjansen, R. Pourhasan and G.W. Semenoff, A holographic quantum Hall ferromagnet, JHEP 02 (2014) 097 [arXiv:1311.6999] [INSPIRE].
A. Karch and L. Randall, Open and closed string interpretation of SUSY CFT’s on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [INSPIRE].
A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156] [INSPIRE].
O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].
J. Erdmenger, Z. Guralnik and I. Kirsch, Four-dimensional superconformal theories with interacting boundaries or defects, Phys. Rev. D 66 (2002) 025020 [hep-th/0203020] [INSPIRE].
J.L. Davis and N. Kim, Flavor-symmetry breaking with charged probes, JHEP 06 (2012) 064 [arXiv:1109.4952] [INSPIRE].
G. Grignani, N. Kim and G.W. Semenoff, D7-anti-D7 bilayer: holographic dynamical symmetry breaking, Phys. Lett. B 722 (2013) 360 [arXiv:1208.0867] [INSPIRE].
J. Sonner, On universality of charge transport in AdS/CFT, JHEP 07 (2013) 145 [arXiv:1304.7774] [INSPIRE].
N. Evans and K.-Y. Kim, Vacuum alignment and phase structure of holographic bi-layers, Phys. Lett. B 728 (2014) 658 [arXiv:1311.0149] [INSPIRE].
V.G. Filev, A quantum critical point from flavours on a compact space, JHEP 08 (2014) 105 [arXiv:1406.5498] [INSPIRE].
V.G. Filev, M. Ihl and D. Zoakos, Holographic bilayer/monolayer phase transitions, JHEP 07 (2014) 043 [arXiv:1404.3159] [INSPIRE].
V.G. Filev, M. Ihl and D. Zoakos, A novel (2+1)-dimensional model of chiral symmetry breaking, JHEP 12 (2013) 072 [arXiv:1310.1222] [INSPIRE].
G. Grignani, A. Marini, N. Kim and G.W. Semenoff, Exciton condensation in a holographic double monolayer semimetal, arXiv:1410.3093 [INSPIRE].
G.W. Semenoff, Condensed matter simulation of a three-dimensional anomaly, Phys. Rev. Lett. 53 (1984) 2449 [INSPIRE].
N. Evans, A. Gebauer, K.-Y. Kim and M. Magou, Phase diagram of the D3/D5 system in a magnetic field and a BKT transition, Phys. Lett. B 698 (2011) 91 [arXiv:1003.2694] [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].
S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [INSPIRE].
G. Grignani, N. Kim and G.W. Semenoff, D3-D5 holography with flux, Phys. Lett. B 715 (2012) 225 [arXiv:1203.6162] [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: 1410.4911
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Grignani, G., Kim, N., Marini, A. et al. Holographic D3-probe-D5 model of a double layer Dirac semimetal. J. High Energ. Phys. 2014, 91 (2014). https://doi.org/10.1007/JHEP12(2014)091
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2014)091