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Holographic topological semimetals

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Abstract

The holographic duality allows to construct and study models of strongly coupled quantum matter via dual gravitational theories. In general such models are characterized by the absence of quasiparticles, hydrodynamic behavior and Planckian dissipation times. One particular interesting class of quantum materials are ungapped topological semimetals which have many interesting properties from Hall transport to topologically protected edge states. We review the application of the holographic duality to this type of quantum matter including the construction of holographic Weyl semimetals, nodal line semimetals, quantum phase transition to trivial states (ungapped and gapped), the holographic dual of Fermi arcs and how new unexpected transport properties, such as Hall viscosities arise. The holographic models promise to lead to new insights into the properties of this type of quantum matter.

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References

  1. O. Vafek, and A. Vishwanath, Annu. Rev. Condens. Matter Phys. 5, 83 (2014).

    Article  ADS  Google Scholar 

  2. P. Hosur, and X. Qi, Compt. Rend. Phys. 14, 857 (2013).

    Article  ADS  Google Scholar 

  3. N. P. Armitage, E. J. Mele, and A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018).

    Article  ADS  Google Scholar 

  4. A. Vishwanath, Physics 8, 84 (2015).

    Article  Google Scholar 

  5. E. Witten, Riv. Nuovo Cim. 39, 313 (2016).

    ADS  Google Scholar 

  6. J. S. Bell, and R. Jackiw, Nuov Cim A 60, 47 (1969).

    Article  ADS  Google Scholar 

  7. S. L. Adler, Phys. Rev. 177, 2426 (1969).

    Article  ADS  Google Scholar 

  8. D. T. Son, and N. Yamamoto, Phys. Rev. Lett. 109, 181602 (2012).

    Article  ADS  Google Scholar 

  9. J. Zaanen, Y. W. Sun, Y. Liu, and K. Schalm, Holographic Duality in Condensed Matter Physics (Cambridge University Press, Cambridge, 2015).

    Book  Google Scholar 

  10. M. Ammon, and J. Erdmenger, Gauge/Gravity Duality: Foundations and Applications (Cambridge University Press, Cambridge, 2015).

    Book  MATH  Google Scholar 

  11. S. A. Hartnoll, A. Lucas, and S. Sachdev, arXiv: 1612.07324.

  12. J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, and U. A. Wiedemann, arXiv: 1101.0618.

  13. R. G. Cai, L. Li, L. F. Li, and R. Q. Yang, Sci. China-Phys. Mech. Astron. 58, 060401 (2015).

    Google Scholar 

  14. R. Baier, P. Romatschke, D. T. Son, A. O. Starinets, and M. A. Stephanov, J. High Energy Phys. 2008, 100 (2008).

    Article  Google Scholar 

  15. M. Rangamani, Class. Quantum Grav. 26, 224003 (2009).

    Article  ADS  Google Scholar 

  16. D. E. Kharzeev, Prog. Particle Nucl. Phys. 75, 133 (2014).

    Article  ADS  Google Scholar 

  17. K. Landsteiner, Acta Phys. Pol. B 47, 2617 (2016).

    Article  ADS  Google Scholar 

  18. J. Erdmenger, M. Haack, M. Kaminski, and A. Yarom, J. High Energy Phys. 2009, 055 (2009).

    Article  Google Scholar 

  19. N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam, and P. Surówka, J. High Energ. Phys. 2011, 94 (2011).

    Article  Google Scholar 

  20. A. Gynther, K. Landsteiner, F. Pena-Benitez, and A. Rebhan, J. High Energ. Phys. 2011, 110 (2011).

    Article  Google Scholar 

  21. K. Landsteiner, E. Megías, and F. Pena-Benitez, Phys. Rev. Lett. 107, 021601 (2011).

    Article  ADS  Google Scholar 

  22. K. Landsteiner, E. Megías, L. Melgar, and F. Pena-Benitez, J. High Energ. Phys. 2011, 121 (2011).

    Article  Google Scholar 

  23. J. Gooth, F. Menges, N. Kumar, V. Sü, C. Shekhar, Y. Sun, U. Drechsler, R. Zierold, C. Felser, and B. Gotsmann, Nat. Commun. 9, 4093 (2018).

    Article  ADS  Google Scholar 

  24. J. Maldacena, Int. J. Theor. Phys. 38, 1113 (1999)

    Article  Google Scholar 

  25. J. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  26. I. R. Klebanov, and E. Witten, Nucl. Phys. B 556, 89 (1999).

    Article  ADS  Google Scholar 

  27. A. G. Grushin, Phys. Rev. D 86, 045001 (2012).

    Article  ADS  Google Scholar 

  28. A. G. Grushin, in Common and not so common high-energy theory methods for condensed matter physics: Topological Matter, Springer Series in Solid-State Sciences, vol 190, edited by D. Bercioux, J. Cayssol, M. Vergniory, and M. Reyes Calvo (Springer, Cham, 2018).

    Google Scholar 

  29. F. D. M. Haldane, Phys. Rev. Lett. 93, 206602 (2004).

    Article  ADS  Google Scholar 

  30. K. Y. Yang, Y. M. Lu, and Y. Ran, Phys. Rev. B 84, 075129 (2011).

    Article  ADS  Google Scholar 

  31. G. Xu, H. Weng, Z. Wang, X. Dai, and Z. Fang, Phys. Rev. Lett. 107, 186806 (2011).

    Article  ADS  Google Scholar 

  32. A. A. Burkov, and L. Balents, Phys. Rev. Lett. 107, 127205 (2011).

    Article  ADS  Google Scholar 

  33. A. A. Zyuzin, and A. A. Burkov, Phys. Rev. B 86, 115133 (2012).

    Article  ADS  Google Scholar 

  34. M. M. Vazifeh, and M. Franz, Phys. Rev. Lett. 111, 027201 (2013).

    Article  ADS  Google Scholar 

  35. F. D. M. Haldane, Nobel lecture: topological phase transitions and topological phases of matter (the Royal Swedish Academy of Sciences, 2016).

  36. R. Jackiw, Int. J. Mod. Phys. B 14, 2011 (2000).

    Article  ADS  Google Scholar 

  37. P. Goswami, and S. Tewari, Phys. Rev. B 88, 245107 (2013).

    Article  ADS  Google Scholar 

  38. A. Jimenez-Alba, K. Landsteiner, Y. Liu, and Y. W. Sun, J. High Energ. Phys. 2015, 117 (2015).

    Article  Google Scholar 

  39. K. Landsteiner, and Y. Liu, Phys. Lett. B 753, 453 (2016).

    Article  ADS  Google Scholar 

  40. K. Landsteiner, Y. Liu, and Y. W. Sun, Phys. Rev. Lett. 116, 081602 (2016).

    Article  ADS  Google Scholar 

  41. C. Copetti, J. Fernández-Pendás, and K. Landsteiner, J. High Energ. Phys. 2017, 138 (2017).

    Article  Google Scholar 

  42. M. Heinrich, A. Jiménez-Alba, S. Moeckel, and M. Ammon, Phys. Rev. Lett. 118, 201601 (2017).

    Article  ADS  Google Scholar 

  43. M. V. Berry, Proc. R. Soc. A-Math. Phys. Eng. Sci. 392, 45 (1984).

    ADS  Google Scholar 

  44. Z. Wang, and S. C. Zhang, Phys. Rev. X 4, 011006 (2014)

    Google Scholar 

  45. Z. Wang, and S. C. Zhang, Phys. Rev. X 2, 031008 (2012).

    Google Scholar 

  46. Z. Wang, and B. Yan, J. Phys.-Condens. Matter 25, 155601 (2013).

    Article  ADS  Google Scholar 

  47. W. Witczak-Krempa, M. Knap, and D. Abanin, Phys. Rev. Lett. 113, 136402 (2014).

    Article  ADS  Google Scholar 

  48. H. Liu, J. McGreevy, and D. Vegh, Phys. Rev. D 83, 065029 (2011).

    Article  ADS  Google Scholar 

  49. M. Čubrović, J. Zaanen, and K. Schalm, Science 325, 439 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  50. Y. Liu, and Y. W. Sun, J. High Energ. Phys. 2018, 189 (2018).

    Article  ADS  Google Scholar 

  51. N. Iqbal, and H. Liu, Fortschr. Phys. 57, 367 (2009).

    Article  MathSciNet  Google Scholar 

  52. G. Song, J. Rong, and S. J. Sin, J. High Energ. Phys. 2019, 109 (2019).

    Article  ADS  Google Scholar 

  53. H. B. Nielsen, and M. Ninomiya, Phys. Lett. B 130, 389 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  54. K. Landsteiner, Y. Liu, and Y. W. Sun, Phys. Rev. Lett. 117, 081604 (2016).

    Article  ADS  Google Scholar 

  55. E. M. Lifschityz, and L. P. Pitaevski, Landau Lifschitz: Course of Theoretical Physics, Volume 10: Physical Kinetics (Butterworth-Heinemann, Oxford, 1981).

    Google Scholar 

  56. J. E. Avron, R. Seiler, and P. G. Zograf, Phys. Rev. Lett. 75, 697 (1995).

    Article  ADS  Google Scholar 

  57. C. Hoyos, Int. J. Mod. Phys. B 28, 1430007 (2014).

    Article  ADS  Google Scholar 

  58. F. M. Haehl, R. Loganayagam, and M. Rangamani, J. High Energ. Phys. 2015, 60 (2015).

    Article  Google Scholar 

  59. A. Cortijo, Y. Ferreirós, K. Landsteiner, and M. A. H. Vozmediano, Phys. Rev. Lett. 115, 177202 (2015).

    Article  ADS  Google Scholar 

  60. P. K. Kovtun, D. T. Son, and A. O. Starinets, Phys. Rev. Lett. 94, 111601 (2005).

    Article  ADS  Google Scholar 

  61. A. Rebhan, and D. Steineder, Phys. Rev. Lett. 108, 021601 (2012).

    Article  ADS  Google Scholar 

  62. S. Jain, N. Kundu, K. Sen, A. Sinha, and S. P. Trivedi, J. High Energ. Phys. 2015, 5 (2015).

    Article  Google Scholar 

  63. C. Copetti, and K. Landsteiner, Phys. Rev. B 99, 195146 (2019).

    Article  ADS  Google Scholar 

  64. X. Ji, Y. Liu, and X. M. Wu, arXiv: 1904.08058.

  65. A. Cortijo, D. Kharzeev, K. Landsteiner, and M. A. H. Vozmediano, Phys. Rev. B 94, 241405 (2016).

    Article  ADS  Google Scholar 

  66. D. I. Pikulin, A. Chen, and M. Franz, Phys. Rev. X 6, 041021 (2016).

    Google Scholar 

  67. A. G. Grushin, J. W. F. Venderbos, A. Vishwanath, and R. Ilan, Phys. Rev. X 6, 041046 (2016).

    Google Scholar 

  68. M. Ammon, M. Baggioli, A. Jimenez-Alba, and S. Moeckel, J. High Energ. Phys. 2018, 68 (2018).

    Article  Google Scholar 

  69. G. Grignani, A. Marini, F. Peña-Benitez, and S. Speziali, J. High Energ. Phys. 2017, 125 (2017).

    Article  Google Scholar 

  70. B. Xu, Y. M. Dai, L. X. Zhao, K. Wang, R. Yang, W. Zhang, J. Y. Liu, H. Xiao, G. F. Chen, A. J. Taylor, D. A. Yarotski, R. P. Prasankumar, and X. G. Qiu, Phys. Rev. B 93, 121110 (2016).

    Article  ADS  Google Scholar 

  71. J. Maldacena, S. H. Shenker, and D. Stanford, J. High Energ. Phys. 2016, 106 (2016).

    Article  Google Scholar 

  72. V. Jahnke, Adv. High Energy Phys. 2019, 9632708 (2019).

    Article  Google Scholar 

  73. M. Baggioli, B. Padhi, P. W. Phillips, and C. Setty, J. High Energ. Phys. 2018, 49 (2018).

    Article  Google Scholar 

  74. B. Roy, P. Goswami, and V. Juričić, Phys. Rev. B 95, 201102 (2017).

    Article  ADS  Google Scholar 

  75. C. Z. Chen, J. Song, H. Jiang, Q. Sun, Z. Wang, and X. C. Xie, Phys. Rev. Lett. 115, 246603 (2015).

    Article  ADS  Google Scholar 

  76. B. Roy, R. J. Slager, and V. Juričić, Phys. Rev. X 8, 031076 (2018).

    Google Scholar 

  77. R. J. Slager, V. Juričić, and B. Roy, Phys. Rev. B 96, 201401(R) (2017).

    Article  ADS  Google Scholar 

  78. Y. Liu, and J. Zhao, J. High Energ. Phys. 2018, 124 (2018).

    Article  ADS  Google Scholar 

  79. E. Kiritsis, and J. Ren, J. High Energ. Phys. 2015, 168 (2015).

    Article  Google Scholar 

  80. C. Charmousis, B. Goutáraux, B. Soo Kim, E. Kiritsis, and R. Meyer, J. High Energ. Phys. 2010, 151 (2010).

    Article  ADS  Google Scholar 

  81. L. Girardello, M. Petrini, M. Porrati, and A. Zaffaroni, J. High Energy Phys. 1999, 026 (1999).

    Article  Google Scholar 

  82. S. A. Hartnoll, and L. Huijse, Class. Quantum Grav. 29, 194001 (2012).

    Article  ADS  Google Scholar 

  83. A. Donos, and S. A. Hartnoll, Nat. Phys. 9, 649 (2013).

    Article  Google Scholar 

  84. A. A. Burkov, M. D. Hook, and L. Balents, Phys. Rev. B 84, 235126 (2011).

    Article  ADS  Google Scholar 

  85. C. Fang, H. Weng, X. Dai, and Z. Fang, Chin. Phys. B 25, 117106 (2016).

    Article  ADS  Google Scholar 

  86. Y. Liu, and Y. W. Sun, J. High Energ. Phys. 2018, 72 (2018).

    Article  Google Scholar 

  87. G. E. Arutyunov, and S. A. Frolov, Phys. Lett. B 441, 173 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  88. R. Alvares, C. Hoyos, and A. Karch, Phys. Rev. D 84, 095020 (2011).

    Article  ADS  Google Scholar 

  89. U. Gürsoy, V. Jacobs, E. Plauschinn, H. Stoof, and S. Vandoren, J. High Energ. Phys. 2013, 127 (2013).

    Article  Google Scholar 

  90. V. P. J. Jacobs, S. J. G. Vandoren, and H. T. C. Stoof, Phys. Rev. B 90, 045108 (2014).

    Article  ADS  Google Scholar 

  91. X. X. Zhang, T. T. Ong, and N. Nagaosa, Phys. Rev. B 94, 235137 (2016).

    Article  ADS  Google Scholar 

  92. H. Hübener, M. A. Sentef, U. De Giovannini, A. F. Kemper, and A. Rubio, Nat. Commun. 8, 13940 (2017).

    Article  ADS  Google Scholar 

  93. K. Hashimoto, S. Kinoshita, K. Murata, and T. Oka, J. High Energ. Phys. 2017, 127 (2017).

    Article  Google Scholar 

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Authors and Affiliations

  1. Instituto de Física Teórica UAM/CSIC, C/Nicolás Cabrera 13–15, Campus Cantoblanco, Cantoblanco, Madrid, 28049, Spain

    Karl Landsteiner

  2. Center for Gravitational Physics, Department of Space Science, Beihang University, Beijing, 100191, China

    Yan Liu

  3. Key Laboratory of Space Environment Monitoring and Information Processing, Ministry of Industry and Information Technology, Beijing, 100191, China

    Yan Liu

  4. School of Physics & CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100049, China

    Ya-Wen Sun

  5. Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Ya-Wen Sun

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  1. Karl Landsteiner
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  2. Yan Liu
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  3. Ya-Wen Sun
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Correspondence to Karl Landsteiner or Yan Liu.

Additional information

This work was supported by the National Key Research and Development Program of China (Grant No. 2018FYA0305800), and the Thousand Young Talents Program of China. The work of Yan Liu was also supported by the National Natural Science Foundation of China (Grant No. 11875083). The work of Ya-Wen Sun has also been partly supported by starting grants from University of Chinese Academy of Sciences and Chinese Academy of Sciences, the Key Research Program of Chinese Academy of Sciences (Grant No. XDPB08-1), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000). The work of Karl Landsteiner was supported by the MCIU/AEI/FEDER, UE (Grant Nos. SEV-2016-0597, FPA2015-65480-P, and PGC2018-095976-B-C21). We would like to thank Daniel Arean, Matteo Baggioli, Rong-Gen Cai, Alberto Cortijo, Chen Fang, Carlos Hoyos, Amadeo Jimenez, Eugenio Megías, Elias Kiritsis, Koenraad Schalm, Francisco Pena-Benitez, Maria Vozmediano, Zhong Wang, Jan Zaanen, FuChun Zhang for useful discussions and C. Copetti, J. Fernandez-Pendás, XuanTing Ji, Xin-Meng Wu and JunKun Zhao for enjoyable collaboration.

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Landsteiner, K., Liu, Y. & Sun, YW. Holographic topological semimetals. Sci. China Phys. Mech. Astron. 63, 250001 (2020). https://doi.org/10.1007/s11433-019-1477-7

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