×

zbMATH — the first resource for mathematics

\(\mathcal{N}\)-extended D = 4 supergravity, unconventional SUSY and graphene. (English) Zbl 1434.83153
Summary: We derive a 2+1 dimensional model with unconventional supersymmetry at the boundary of an \(\mathrm{AdS}_4\) \(\mathcal{N}\)-extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model is instrumental in describing, within a top-down approach, the electronic properties of graphene-like 2D materials at the two Dirac points, \(\mathbf{K}\) and \(\mathbf{K} '\). The two valleys correspond to the two independent sectors of the \(\mathrm{OSp}(p \vert 2) \times \mathrm{OSp} (q \vert 2)\) boundary model in the \(p = q\) case, which are related by a parity transformation. The Semenoff and Haldane-type masses entering the corresponding Dirac equations are identified with the torsion parameters of the substrate in the model.

MSC:
83E50 Supergravity
81T60 Supersymmetric field theories in quantum mechanics
58J28 Eta-invariants, Chern-Simons invariants
83E05 Geometrodynamics and the holographic principle
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Achúcarro, A.; Townsend, Pk, A Chern-Simons Action for Three-Dimensional anti-de Sitter Supergravity Theories, Phys. Lett., B 180, 89 (1986)
[2] Gaiotto, D.; Witten, E., Janus Configurations, Chern-Simons Couplings, And The theta-Angle in N = 4 Super Yang-Mills Theory, JHEP, 06, 097 (2010) · Zbl 1290.81065
[3] Kapustin, A.; Saulina, N., Chern-Simons-Rozansky-Witten topological field theory, Nucl. Phys., B 823, 403 (2009) · Zbl 1196.81211
[4] J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [Adv. Theor. Math. Phys.2 (1998) 231] [hep-th/9711200] [INSPIRE]. · Zbl 0914.53047
[5] Gubser, Ss; Klebanov, Ir; Polyakov, Am, Gauge theory correlators from noncritical string theory, Phys. Lett., B 428, 105 (1998) · Zbl 1355.81126
[6] Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048
[7] Álvarez, Pd; Valenzuela, M.; Zanelli, J., Supersymmetry of a different kind, JHEP, 04, 058 (2012) · Zbl 1348.81394
[8] Guevara, A.; Pais, P.; Zanelli, J., Dynamical Contents of Unconventional Supersymmetry, JHEP, 08, 085 (2016) · Zbl 1390.81193
[9] Iorio, A.; Lambiase, G., The Hawking-Unruh phenomenon on graphene, Phys. Lett., B 716, 334 (2012)
[10] Álvarez, Pd; Pais, P.; Zanelli, J., Unconventional supersymmetry and its breaking, Phys. Lett., B 735, 314 (2014) · Zbl 1380.81199
[11] Gomes, Ymp; Helayel-Neto, Ja, On a five-dimensional Chern-Simons AdS supergravity without gravitino, Phys. Lett., B 777, 275 (2018) · Zbl 1411.83133
[12] Andrianopoli, L.; Cerchiai, Bl; D’Auria, R.; Trigiante, M., Unconventional supersymmetry at the boundary of AdS4 supergravity, JHEP, 04, 007 (2018) · Zbl 1390.83359
[13] M. Ezawa, Supersymmetry and unconventional quantum Hall effect in graphene, Phys. Lett.A 372 (2008) 924 [cond-mat/0606084] [INSPIRE].
[14] S.-S. Lee, Emergence of supersymmetry at a critical point of a lattice model, Phys. Rev.B 76 (2007) 075103 [cond-mat/0611658] [INSPIRE].
[15] Dartora, Ca; Cabrera, Gg, Wess-Zumino supersymmetric phase and superconductivity in graphene, Phys. Lett., A 377, 907 (2013) · Zbl 1298.81101
[16] Andrianopoli, L.; Cerchiai, Bl; Grassi, Pa; Trigiante, M., The Quantum Theory of Chern-Simons Supergravity, JHEP, 06, 036 (2019) · Zbl 1416.83133
[17] A. Iorio and P. Pais, (Anti-)de Sitter, Poincaré, Super symmetries and the two Dirac points of graphene, Annals Phys.398 (2018) 265 [arXiv:1807.08764] [INSPIRE]. · Zbl 1404.81190
[18] Andrianopoli, L.; D’Auria, R., N = 1 and N = 2 pure supergravities on a manifold with boundary, JHEP, 08, 012 (2014)
[19] H.T. Nieh and M.L. Yan, Quantized Dirac Field in Curved Riemann-Cartan Background. 1. Symmetry Properties, Green’s Function, Annals Phys.138 (1982) 237 [INSPIRE].
[20] Chandía, O.; Zanelli, J., Topological invariants, instantons and chiral anomaly on spaces with torsion, Phys. Rev., D 55, 7580 (1997)
[21] T.L. Hughes, R.G. Leigh and O. Parrikar, Torsional Anomalies, Hall Viscosity and Bulk-boundary Correspondence in Topological States, Phys. Rev.D 88 (2013) 025040 [arXiv:1211.6442] [INSPIRE].
[22] Parrikar, O.; Hughes, Tl; Leigh, Rg, Torsion, Parity-odd Response and Anomalies in Topological States, Phys. Rev., D 90, 105004 (2014)
[23] Novoselov, Ks, Electric field effect in atomically thin carbon films, Science, 306, 666 (2004)
[24] Novoselov, Ks, Two-dimensional atomic crystals, Proc. Nat. Acad. Sci., 102, 10451 (2005)
[25] Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K., The electronic properties of graphene, Reviews of Modern Physics, 81, 1, 109-162 (2009)
[26] Katsnelson, M.; Novoselov, Ks, Graphene: New bridge between condensed matter physics and quantum electrodynamics, Solid State Commun., 143, 3 (2007)
[27] Vozmediano, Mah; Katsnelson, M.; Guinea, F., Gauge fields in graphene, Phys. Rept., 496, 109 (2010)
[28] A. Cortijo and M.A.H. Vozmediano, Effects of topological defects and local curvature on the electronic properties of planar graphene, Nucl. Phys.B 763 (2007) 293 [Erratum ibid.B 807 (2009) 659] [cond-mat/0612374] [INSPIRE]. · Zbl 1116.82335
[29] K.S. Novoselov et al., Two-dimensional gas of massless Dirac fermions in graphene, Nature438 (2005) 197 [cond-mat/0509330] [INSPIRE].
[30] Y. Zhang, Y.-W. Tan, H.L. Stormer and P. Kim, Experimental observation of the quantum Hall effect and and Berry’s phase in graphene, Nature438 (2005) 201 [cond-mat/0509355] [INSPIRE].
[31] V.P. Gusynin, S.G. Sharapov and J.P. Carbotte, Unusual microwave response of Dirac quasiparticles in graphene, Phys. Rev. Lett.96 (2006) 256802 [cond-mat/0603267] [INSPIRE].
[32] A. Iorio and G. Lambiase, Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect and all that, Phys. Rev.D 90 (2014) 025006 [arXiv:1308.0265] [INSPIRE].
[33] Geim, Ak; Novoselov, Ks, The rise of graphene, Nat. Mater., 6, 183 (2007)
[34] Boada, O.; Celi, A.; Latorre, Ji; Lewenstein, M., Dirac Equation For Cold Atoms In Artificial Curved Spacetimes, New J. Phys., 13, 035002 (2011)
[35] Iorio, A., Weyl-Gauge Symmetry of Graphene, Annals Phys., 326, 1334 (2011) · Zbl 1221.81130
[36] Gallerati, A., Graphene properties from curved space Dirac equation, Eur. Phys. J. Plus, 134, 202 (2019)
[37] M.F. Ciappina, A. Iorio, P. Pais and A. Zampeli, Torsion in quantum field theory through time-loops on Dirac materials, arXiv:1907.00023 [INSPIRE].
[38] Semenoff, Gw, Condensed Matter Simulation of a Three-dimensional Anomaly, Phys. Rev. Lett., 53, 2449 (1984)
[39] G. Giovannetti, P.A. Khomyakov, G. Brocks, P.J. Kelly and J. van den Brink, Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations, Phys. Rev.B 76 (2007) 073103.
[40] Zhou, Sy, Substrate-induced bandgap opening in epitaxial graphene, Nat. Mater., 6, 770 (2007)
[41] Haldane, Fdm, Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the ‘Parity Anomaly’, Phys. Rev. Lett., 61, 2015 (1988)
[42] R. Noris and L. Fatibene, Spin frame transformations and Dirac equations, arXiv:1910.04634 [INSPIRE].
[43] Jotzu, G., Experimental realization of the topological haldane model with ultracold fermions, Nature, 515, 237 (2014)
[44] H.-S. Kim and H.-Y. Kee, Realizing Haldane model in Fe-based honeycomb ferromagnetic insulators, npj Quantum Mater.2 (2017) 20.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.