Abstract
Floquet states can be realized in quantum systems driven by continuous time-periodic perturbations. It is known that a state known as the Floquet Weyl semimetal can be realized when free Dirac fermions are placed in a rotating electric field. What will happen if strong interaction is introduced to this system? Will the interaction wash out the characteristic features of Weyl semimetals such as the Hall response? Is there a steady state and what is its thermodynamic behavior? We answer these questions using AdS/CFT correspondence in the \( \mathcal{N} \) = 2 supersymmetric massless QCD in a rotating electric field in the large N c limit realizing the first example of a “holographic Floquet state”. In this limit, gluons not only mediate interaction, but also act as an energy reservoir and stabilize the nonequilibrium steady state (NESS). We obtain the electric current induced by a rotating electric field: in the high frequency region, the Ohm’s law is satisfied, while we recover the DC nonlinear conductivity at low frequency, which was obtained holographically in a previous work. The thermodynamic properties of the NESS, e.g., fluctuation-dissipation relation, is characterized by the effective Hawking temperature that is defined from the effective horizon giving a holographic meaning to the “periodic thermodynamic” concept. In addition to the strong (pump) rotating electric field, we apply an additional weak (probe) electric field in the spirit of the pump-probe experiments done in condensed matter experiments. Weak DC and AC probe analysis in the background rotating electric field shows Hall currents as a linear response, therefore the Hall response of Floquet Weyl semimetals survives at the strong coupling limit. We also find frequency mixed response currents, i.e., a heterodyning effect, characteristic to periodically driven Floquet systems.
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].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
M. Cubrović, J. Zaanen and K. Schalm, String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid, Science 325 (2009) 439 [arXiv:0904.1993] [INSPIRE].
L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].
J. Sonner and A.G. Green, Hawking Radiation and Non-equilibrium Quantum Critical Current Noise, Phys. Rev. Lett. 109 (2012) 091601 [arXiv:1203.4908] [INSPIRE].
H. Sambe, Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field, Phys. Rev. A 7 (1973) 2203.
N.H. Lindner, G. Refael and V. Galitski, Floquet topological insulator in semiconductor quantum wells, Nat. Phys. 7 (2011) 490.
T. Oka and H. Aoki, Photovoltaic Hall effect in graphene, Phys. Rev. B 79 (2009) 081406R.
T. Kitagawa, M.S. Rudner, E. Berg and E. Demler, Exploring topological phases with quantum walks, Phys. Rev. A 82 (2010) 033429.
T. Kitagawa, T. Oka, A. Brataas, L. Fu and E. Demler, Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels, Phys. Rev. B 84 (2011) 235108 [arXiv:1104.4636].
F.D.M. Haldane, Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the ‘Parity Anomaly’, Phys. Rev. Lett. 61 (1988) 2015 [INSPIRE].
G. Jotzu et al., Experimental realization of the topological Haldane model with ultracold fermions, Nature 515 (2014) 237 [arXiv:1406.7874].
Y.H. Wang, H. Steinberg, P. Jarillo-Herrero and N. Gedik, Observation of Floquet-Bloch states on the surface of a topological insulator, Science 342 (2013) 453 [arXiv:1310.7563] [INSPIRE].
H.B. Nielsen and M. Ninomiya, Adler-Bell-Jackiw anomaly and Weyl fermions in crystal, Phys. Lett. B 130 (1983) 389 [INSPIRE].
R. Wang, B. Wang, R. Shen, L. Sheng and D.Y. Xing Floquet Weyl semimetal induced by topological phase transitions, Europhys. Lett. 105 (2014) 17004 [arXiv:1308.4266].
X.-X. Zhang, T.T. Ong and N. Nagaosa, Theory of photoinduced Floquet Weyl semimetal phases, Phys. Rev. B 94 (2016) 235137 [arXiv:1607.05941] [INSPIRE].
H. Hübener, M.A. Sentef, U. de Giovannini, A.F. Kemper and A. Rubio, Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials, Nat. Commun. 8 (2017) 13940 [arXiv:1604.03399].
L. Bucciantini, S. Roy, S. Kitamura, T. Oka and L. Bucciantini, to appear.
Z. Yan and Z. Wang, Tunable Weyl Points in Periodically Driven Nodal Line Semimetals, Phys. Rev. Lett. 117 (2016) 087402 [arXiv:1605.04404].
W. Kohn, Periodic thermodynamics, J. Stat. Phys. 103 (2014) 417.
A. Lazarides, A. Das and R. Moessner, Periodic thermodynamics of isolated systems, Phys. Rev. Lett. 112 (2014) 150401 [arXiv:1401.0164].
A. Lazarides, A. Das and R. Moessner, Equilibrium states of generic quantum systems subject to periodic driving, Phys. Rev. E 90 (2014) 012110.
L. D’Alessio and M. Rigol, Long-time Behavior of Isolated Periodically Driven Interacting Lattice Systems, Phys. Rev. X 4 (2014) 041048.
H. Dehghani, T. Oka and A. Mitra, Dissipative Floquet topological systems, Phys. Rev. B 90 (2014) 195429.
H. Dehghani and A. Mitra, Optical Hall conductivity of a Floquet topological insulator, Phys. Rev. B 92 (2015) 165111 [arXiv:1506.08687].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
K. Landsteiner and Y. Liu, The holographic Weyl semi-metal, Phys. Lett. B 753 (2016) 453 [arXiv:1505.04772] [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Quarks in an external electric field in finite temperature large-N gauge theory, JHEP 08 (2008) 092 [arXiv:0709.1554] [INSPIRE].
J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with flavour in electric and magnetic Kalb-Ramond fields, JHEP 12 (2007) 091 [arXiv:0709.1551] [INSPIRE].
K. Hashimoto and T. Oka, Vacuum Instability in Electric Fields via AdS/CFT: Euler-Heisenberg Lagrangian and Planckian Thermalization, JHEP 10 (2013) 116 [arXiv:1307.7423] [INSPIRE].
K. Hashimoto, T. Oka and A. Sonoda, Magnetic instability in AdS/CFT: Schwinger effect and Euler-Heisenberg Lagrangian of supersymmetric QCD, JHEP 06 (2014) 085 [arXiv:1403.6336] [INSPIRE].
K. Hashimoto, T. Oka and A. Sonoda, Electromagnetic instability in holographic QCD, JHEP 06 (2015) 001 [arXiv:1412.4254] [INSPIRE].
K. Hashimoto, S. Kinoshita, K. Murata and T. Oka, Electric Field Quench in AdS/CFT, JHEP 09 (2014) 126 [arXiv:1407.0798] [INSPIRE].
K. Hashimoto, S. Kinoshita, K. Murata and T. Oka, Turbulent meson condensation in quark deconfinement, Phys. Lett. B 746 (2015) 311 [arXiv:1408.6293] [INSPIRE].
K. Hashimoto, S. Kinoshita, K. Murata and T. Oka, Meson turbulence at quark deconfinement from AdS/CFT, Nucl. Phys. B 896 (2015) 738 [arXiv:1412.4964] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [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, 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. Sachdev, Condensed Matter and AdS/CFT, arXiv:1002.2947 [INSPIRE].
W.-J. Li, Y. Tian and H.-b. Zhang, Periodically Driven Holographic Superconductor, JHEP 07 (2013) 030 [arXiv:1305.1600] [INSPIRE].
M. Natsuume and T. Okamura, The enhanced holographic superconductor: is it possible?, JHEP 08 (2013) 139 [arXiv:1307.6875] [INSPIRE].
T. Oka and L. Bucciantini, Heterodyne Hall effect in a two-dimensional electron gas, Phys. Rev. B 94 (2016) 155133 [arXiv:1607.01041].
J.H. Shirley, Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time, Phys. Rev. 138 (1965) B979.
T. Morimoto and N. Nagaosa, Weyl Mott Insulator, Sci. Rep. 6 (2016) 19853 [arXiv:1508.03203].
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].
A. Karch, A. O’Bannon and E. Thompson, The Stress-Energy Tensor of Flavor Fields from AdS/CFT, JHEP 04 (2009) 021 [arXiv:0812.3629] [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].
G.W. Gibbons, Pulse propagation in Born-Infeld theory: The World volume equivalence principle and the Hagedorn-like equation of state of the Chaplygin gas, Grav. Cosmol. 8 (2002) 2 [hep-th/0104015] [INSPIRE].
G. Gibbons, K. Hashimoto and P. Yi, Tachyon condensates, Carrollian contraction of Lorentz group and fundamental strings, JHEP 09 (2002) 061 [hep-th/0209034] [INSPIRE].
T. Oka and H. Aoki, All Optical Measurement Proposed for the Photovoltaic Hall Effect, J. Phys. Conf. Ser. 334 (2011) 012060 [arXiv:1007.5399].
A.A. Burkov and L. Balents, Weyl Semimetal in a Topological Insulator Multilayer, Phys. Rev. Lett. 107 (2011) 127205 [arXiv:1105.5138] [INSPIRE].
K. Hashimoto, S. Kinoshita, K. Murata and T. Oka, in preparation.
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: 1611.03702
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
Hashimoto, K., Kinoshita, S., Murata, K. et al. Holographic Floquet states I: a strongly coupled Weyl semimetal. J. High Energ. Phys. 2017, 127 (2017). https://doi.org/10.1007/JHEP05(2017)127
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2017)127