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Journal of High Energy Physics

, 2018:72 | Cite as

Topological nodal line semimetals in holography

  • Yan Liu
  • Ya-Wen SunEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We show a holographic model of a strongly coupled topological nodal line semimetal (NLSM) and find that the NLSM phase could go through a quantum phase transition to a topologically trivial state. The dual fermion spectral function shows that there are multiple Fermi surfaces each of which is a closed nodal loop in the NLSM phase. The topological structure in the bulk is induced by the IR interplay between the dual mass operator and the operator that deforms the topology of the Fermi surface. We propose a practical framework for building various strongly coupled topological semimetals in holography, which indicates that at strong coupling topologically nontrivial semimetal states generally exist.

Keywords

Holography and condensed matter physics (AdS/CMT) AdS-CFT Correspondence 

Notes

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.

References

  1. [1]
    E. Witten, Three Lectures On Topological Phases Of Matter, Riv. Nuovo Cim. 39 (2016) 313 [arXiv:1510.07698] [INSPIRE].ADSGoogle Scholar
  2. [2]
    C.-K. Chiu, J.C. Teo, A.P. Schnyder and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88 (2016) 035005 [arXiv:1505.03535] [INSPIRE].
  3. [3]
    W. Witczak-Krempa, M. Knap and D. Abanin, Interacting Weyl semimetals: characterization via the topological Hamiltonian and its breakdown, Phys. Rev. Lett. 113 (2014) 136402 [arXiv:1406.0843] [INSPIRE].
  4. [4]
    J. Liu and L. Balents, Correlation and transport phenomena in topological nodal-loop semimetals, Phys. Rev. B 95 (2017) 075426 [arXiv:1609.05529].
  5. [5]
    J. Zaanen, Y.W. Sun, Y. Liu and K. Schalm, Holographic Duality in Condensed Matter Physics, Cambridge University Press, (2015).Google Scholar
  6. [6]
    M. Ammon and J. Erdmenger, Gauge/gravity duality: Foundations and applications, Cambridge University Press, (2015).Google Scholar
  7. [7]
    S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
  8. [8]
    C. Hoyos-Badajoz, K. Jensen and A. Karch, A Holographic Fractional Topological Insulator, Phys. Rev. D 82 (2010) 086001 [arXiv:1007.3253] [INSPIRE].
  9. [9]
    C. Kristjansen and G.W. Semenoff, The D3-probe-D7 brane holographic fractional topological insulator, JHEP 10 (2016) 079 [arXiv:1604.08548] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Y. Seo, G. Song and S.-J. Sin, Strong Correlation Effects on Surfaces of Topological Insulators via Holography, Phys. Rev. B 96 (2017) 041104 [arXiv:1703.07361] [INSPIRE].
  11. [11]
    M. Fujita, W. Li, S. Ryu and T. Takayanagi, Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy, JHEP 06 (2009) 066 [arXiv:0901.0924] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Quantum Hall Effect in a Holographic Model, JHEP 10 (2010) 063 [arXiv:1003.4965] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  13. [13]
    K. Landsteiner, Y. Liu and Y.-W. Sun, Quantum phase transition between a topological and a trivial semimetal from holography, Phys. Rev. Lett. 116 (2016) 081602 [arXiv:1511.05505] [INSPIRE].
  14. [14]
    K. Landsteiner, Y. Liu and Y.-W. Sun, Odd viscosity in the quantum critical region of a holographic Weyl semimetal, Phys. Rev. Lett. 117 (2016) 081604 [arXiv:1604.01346] [INSPIRE].
  15. [15]
    C. Copetti, J. Fernández-Pendás and K. Landsteiner, Axial Hall effect and universality of holographic Weyl semi-metals, JHEP 02 (2017) 138 [arXiv:1611.08125] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    M. Ammon, M. Heinrich, A. Jiménez-Alba and S. Moeckel, Surface States in Holographic Weyl Semimetals, Phys. Rev. Lett. 118 (2017) 201601 [arXiv:1612.00836] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    K. Landsteiner and Y. Liu, The holographic Weyl semi-metal, Phys. Lett. B 753 (2016) 453 [arXiv:1505.04772] [INSPIRE].
  18. [18]
    G. Grignani, A. Marini, F. Pena-Benitez and S. Speziali, AC conductivity for a holographic Weyl Semimetal, JHEP 03 (2017) 125 [arXiv:1612.00486] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    A.A. Burkov, M.D. Hook and L. Balents, Topological nodal semimetals, Phys. Rev. B 84 (2011) 235126 [arXiv:1110.1089].
  20. [20]
    C. Fang, H. Weng, X. Dai and Z. Fang, Topological nodal line semimetals, Chin. Phys. B 25 (2016) 117106 [arXiv:1609.05414].
  21. [21]
    R. Alvares, C. Hoyos and A. Karch, An improved model of vector mesons in holographic QCD, Phys. Rev. D 84 (2011) 095020 [arXiv:1108.1191] [INSPIRE].
  22. [22]
    S. Grozdanov and N. Poovuttikul, Generalised global symmetries and magnetohydrodynamic waves in a strongly interacting holographic plasma, arXiv:1707.04182 [INSPIRE].
  23. [23]
    D.M. Hofman and N. Iqbal, Generalized global symmetries and holography, SciPost Phys. 4 (2018) 005 [arXiv:1707.08577] [INSPIRE].
  24. [24]
    R.-G. Cai and R.-Q. Yang, Paramagnetism-Ferromagnetism Phase Transition in a Dyonic Black Hole, Phys. Rev. D 90 (2014) 081901 [arXiv:1404.2856] [INSPIRE].
  25. [25]
    N. Iqbal, H. Liu and M. Mezei, Quantum phase transitions in semilocal quantum liquids, Phys. Rev. D 91 (2015) 025024 [arXiv:1108.0425] [INSPIRE].
  26. [26]
    A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
  27. [27]
    S.A. Hartnoll and L. Huijse, Fractionalization of holographic Fermi surfaces, Class. Quant. Grav. 29 (2012) 194001 [arXiv:1111.2606] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    Y. Liu, K. Schalm, Y.-W. Sun and J. Zaanen, Bose-Fermi competition in holographic metals, JHEP 10 (2013) 064 [arXiv:1307.4572] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    N. Iqbal and H. Liu, Real-time response in AdS/CFT with application to spinors, Fortsch. Phys. 57 (2009) 367 [arXiv:0903.2596] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev. D 83 (2011) 065029 [arXiv:0903.2477] [INSPIRE].
  31. [31]
    M. Cubrovic, J. Zaanen and K. Schalm, String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid, Science 325 (2009) 439 [arXiv:0904.1993] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    Y. Liu and Y.-W. Sun, Topological invariants for holographic semimetals, JHEP 10 (2018) 189 [arXiv:1809.00513] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  33. [33]
    Z. Wang and S.-C. Zhang, Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus, Phys. Rev. X 4 (2014) 011006 [arXiv:1308.4900] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Space Science, and International Research Institute of Multidisciplinary ScienceBeihang UniversityBeijingChina
  2. 2.School of physics & CAS Center for Excellence in Topological Quantum ComputationUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.Kavli Insititute for Theoretical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  4. 4.CAS Key Laboratory of Theoretical Physics, Institute of Theoretical PhysicsChinese Academy of SciencesBeijingChina

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