Abstract
We use the AdS/CFT correspondence to compute the AC conductivities for a (2+1)-dimensional system of massless fundamental fermions coupled to (3+1)-dimensional Super Yang-Mills theory at strong coupling. We consider the system at finite charge density, with a constant electric field along the defect and an orthogonal magnetic field. The holographic model we employ is the well studied D3/probe-D5-brane system. There are two competing phases in this model: a phase with broken chiral symmetry favored when the magnetic field dominates over the charge density and the electric field and a chirally symmetric phase in the opposite regime. The presence of the electric field induces Ohm and Hall currents, which can be straightforwardly computed by means of the Karch-O’Bannon technique. Studying the fluctuations around the stable configurations in linear response theory, we are able to derive the full frequency dependence of longitudinal and Hall conductivities in all the regions of the phase space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
J. Crossno et al., Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene, Science 351 (2016) 1058 [arXiv:1509.04713].
R.V. Gorbachev et al., Strong Coulomb drag and broken symmetry in double-layer graphene, Nature Phys. 8 (2012) 896.
Y. Seo, G. Song, P. Kim, S. Sachdev and S.-J. Sin, Holography of the Dirac Fluid in Graphene with two currents, Phys. Rev. Lett. 118 (2017) 036601 [arXiv:1609.03582] [INSPIRE].
M. Rogatko and K.I. Wysokinski, Two interacting current model of holographic Dirac fluid in graphene, Phys. Rev. D 97 (2018) 024053 [arXiv:1708.08051] [INSPIRE].
M. Rogatko and K.I. Wysokinski, Holographic calculation of the magneto-transport coefficients in Dirac semimetals, JHEP 01 (2018) 078 [arXiv:1712.01608] [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].
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].
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].
V.G. Filev, C.V. Johnson, R.C. Rashkov and K.S. Viswanathan, Flavoured large N gauge theory in an external magnetic field, JHEP 10 (2007) 019 [hep-th/0701001] [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].
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].
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].
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].
G. Grignani, N. Kim, A. Marini and G.W. Semenoff, Holographic D3-probe-D5 Model of a Double Layer Dirac Semimetal, JHEP 12 (2014) 091 [arXiv:1410.4911] [INSPIRE].
G. Grignani, A. Marini, A.-C. Pigna and G.W. Semenoff, Phase structure of a holographic double monolayer Dirac semimetal, JHEP 06 (2016) 141 [arXiv:1603.02583] [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
N. Evans, K.-Y. Kim, J.P. Shock and J.P. Shock, Chiral phase transitions and quantum critical points of the D3/D7(D5) system with mutually perpendicular E and B fields at finite temperature and density, JHEP 09 (2011) 021 [arXiv:1107.5053] [INSPIRE].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].
S.R. Das, T. Nishioka and T. Takayanagi, Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT, JHEP 07 (2010) 071 [arXiv:1005.3348] [INSPIRE].
A. O’Bannon, Hall Conductivity of Flavor Fields from AdS/CFT, Phys. Rev. D 76 (2007) 086007 [arXiv:0708.1994] [INSPIRE].
D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [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].
J. Mas, J.P. Shock, J. Tarrio and D. Zoakos, Holographic Spectral Functions at Finite Baryon Density, JHEP 09 (2008) 009 [arXiv:0805.2601] [INSPIRE].
K.-Y. Kim, J.P. Shock and J. Tarrio, The open string membrane paradigm with external electromagnetic fields, JHEP 06 (2011) 017 [arXiv:1103.4581] [INSPIRE].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
G.W. Gibbons and C.A.R. Herdeiro, Born-Infeld theory and stringy causality, Phys. Rev. D 63 (2001) 064006 [hep-th/0008052] [INSPIRE].
S. Ryu, T. Takayanagi and T. Ugajin, Holographic Conductivity in Disordered Systems, JHEP 04 (2011) 115 [arXiv:1103.6068] [INSPIRE].
C.-F. Chen and A. Lucas, Origin of the Drude peak and of zero sound in probe brane holography, Phys. Lett. B 774 (2017) 569 [arXiv:1709.01520] [INSPIRE].
S. Grozdanov, A. Lucas and N. Poovuttikul, Holography and hydrodynamics with weakly broken symmetries, arXiv:1810.10016 [INSPIRE].
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
P. Bøggild et al., Mapping the electrical properties of large-area graphene, 2D Materials 4 (2017) 042003.
J. Horng et al., Drude conductivity of Dirac fermions in graphene, Phys. Rev. B 83 (2011) 165113.
S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev. D 76 (2007) 066001 [arXiv:0704.1160] [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: 1807.10717
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Grignani, G., Marini, A., Papini, L. et al. AC conductivities of a holographic Dirac semimetal. J. High Energ. Phys. 2018, 109 (2018). https://doi.org/10.1007/JHEP12(2018)109
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2018)109