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Review of recent progress on THz spectroscopy of quantum materials: superconductors, magnetic and topological materials

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A Correction to this article was published on 10 January 2024

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Abstract

Recently, the THz spectroscopy has been efficiently used to investigate varieties of quantum materials, including superconductors, novel magnetic, and topological materials. These materials often exhibit strong correlation and competing interactions between various degrees of freedom, including charge, spins, orbital, and lattice dynamics, which lead to many exotic phenomena and novel phase transitions whose cause–effect correlations are challenging to determine. Whereas probing the ground state’s excitations can unravel the underlying mechanism of these complex phenomena. The characteristic energy scales of different elementary excitations and collective modes in many of these materials are in the THz frequency range. Therefore, THz spectroscopy has become a very effective probe and directly revealed many exciting physics. Many novel phenomena, including exotic quasiparticle excitations in magnetic systems, topological magneto-electric effect, and topological quantum phase transition in three-dimensional topological insulators, are studied with unprecedented success. Here, we review some recent research reports on many-body quantum materials, including superconductors, novel magnetic, and topological materials probed by few popular THz-spectroscopy techniques. We will also briefly discuss the prospects of using THz spectroscopy for observing some exotic quantum phenomena that are still elusive or under investigation.

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References

  1. N. Physics, The rise of quantum materials (2016). https://doi.org/10.1038/nphys3668

  2. R. Sinatra, P. Deville, M. Szell, D. Wang, A.L. Barabási, Nat. Phys. 11(10), 791 (2015). https://doi.org/10.1038/nphys3494

    Article  Google Scholar 

  3. B. Keimer, J.E. Moore, Nat. Phys. 13(11), 1045 (2017). https://doi.org/10.1038/nphys4302

    Article  Google Scholar 

  4. N. Samarth, Nat. Mater. 16(11), 1068 (2017). https://doi.org/10.1038/nmat5010

    Article  ADS  Google Scholar 

  5. K.A. Moler, Nat. Mater. 16(11), 1049 (2017). https://doi.org/10.1038/nmat5018

    Article  ADS  Google Scholar 

  6. Y. Tokura, M. Kawasaki, N. Nagaosa, Nat. Phys. 13(11), 1056 (2017). https://doi.org/10.1038/nphys4274

    Article  Google Scholar 

  7. S. Mhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, P.Böni, Science 323(5916), 915 (2009). http://science.sciencemag.org/content/323/5916/915.abstract

  8. W. Witczak-Krempa, G. Chen, Y.B. Kim, L. Balents, Ann. Rev. Condens. Matter Phys. 5(1), 57 (2014). https://doi.org/10.1146/annurev-conmatphys-020911-125138

    Article  ADS  Google Scholar 

  9. M.Z. Hasan, J.E. Moore, Ann. Rev. Condens. Matter Phys. 2(1), 55 (2011). https://doi.org/10.1146/annurev-conmatphys-062910-140432

    Article  ADS  Google Scholar 

  10. B. Yan, C. Felser, Ann. Rev. Condens. Matter Phys. 8(1), 337 (2017). https://doi.org/10.1146/annurev-conmatphys-031016-025458

    Article  ADS  Google Scholar 

  11. N.P. Armitage, E.J. Mele, A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018). https://doi.org/10.1103/RevModPhys.90.015001

    Article  ADS  Google Scholar 

  12. G. Wendin, Rep. Progr. Phys. 80(10), 106001 (2017). https://doi.org/10.1088/1361-6633/aa7e1a

    Article  ADS  MathSciNet  Google Scholar 

  13. P. Ball, MRS Bull. 42(10), 698 (2017). https://doi.org/10.1557/mrs.2017.220

    Article  ADS  Google Scholar 

  14. E. Dagotto, Science 309(5732), 257 (2005). https://doi.org/10.1126/science.1107559. https://science.sciencemag.org/content/309/5732/257

  15. D.N. Basov, R.D. Averitt, D. Hsieh, Nat. Mater. 16(11), 1077 (2017). https://doi.org/10.1038/nmat5017

    Article  ADS  Google Scholar 

  16. A. Damascelli, Z. Hussain, Z.X. Shen, Rev. Mod. Phys. 75, 473 (2003). https://doi.org/10.1103/RevModPhys.75.473

    Article  ADS  Google Scholar 

  17. G. Binnig, H. Rohrer, Rev. Mod. Phys. 59, 615 (1987). https://doi.org/10.1103/RevModPhys.59.615

    Article  ADS  Google Scholar 

  18. S.W. Lovesey, Theory of neutron scattering from condensed matter (Clarendon Press, United Kingdom, 1984). http://inis.iaea.org/search/search.aspx?orig_q=RN:16036521

  19. M. Mondal, A. Kamlapure, S.C. Ganguli, J. Jesudasan, V. Bagwe, L. Benfatto, P. Raychaudhuri, Sci. Rep. 3, 1 (2013). https://doi.org/10.1038/srep01357

    Article  Google Scholar 

  20. D.N. Basov, T. Timusk, Rev. Mod. Phys. 77, 721 (2005). https://doi.org/10.1103/RevModPhys.77.721

    Article  ADS  Google Scholar 

  21. D.N. Basov, R.D. Averitt, D. van der Marel, M. Dressel, K. Haule, Rev. Mod. Phys. 83, 471 (2011). https://doi.org/10.1103/RevModPhys.83.471

    Article  ADS  Google Scholar 

  22. Y. Liu, N.O. Weiss, X. Duan, H.C. Cheng, Y. Huang, X. Duan, Nat. Rev. Mater. 1(9), 16042 (2016). https://doi.org/10.1038/natrevmats.2016.42

    Article  ADS  Google Scholar 

  23. D. Nicoletti, A. Cavalleri, Adv. Opt. Photon. 8(3), 401 (2016). https://doi.org/10.1364/AOP.8.000401. http://aop.osa.org/abstract.cfm?URI=aop-8-3-401

  24. R. Shimano, N. Tsuji, Ann. Rev. Condens. Matter Phys. 11(1), 103 (2020). https://doi.org/10.1146/annurev-conmatphys-031119-050813

    Article  ADS  Google Scholar 

  25. Y. Kawano, Contemp. Phys. 54(3), 143 (2013). https://doi.org/10.1080/00107514.2013.817194

    Article  ADS  Google Scholar 

  26. K.S. Kumar, G.L. Prajapati, R. Dagar, M. Vagadia, D.S. Rana, M. Tonouchi, Adv. Opt. Mater. 8(3), 1900958 (2020). https://doi.org/10.1002/adom.201900958

    Article  Google Scholar 

  27. C.A. Schmuttenmaer, Chem. Rev. 104(4), 1759 (2004). https://doi.org/10.1021/cr020685g

    Article  Google Scholar 

  28. M. Hangyo, T. Nagashima, S. Nashima, Measur. Sci. Technol. 13(11), PII (2002). https://doi.org/10.1088/0957-0233/13/11/309

  29. D. Dragoman, M. Dragoman, Progr. Quantum Electron. 28(1), 1 (2004). https://doi.org/10.1016/S0079-6727(03)00058-2. http://www.sciencedirect.com/science/article/pii/S0079672703000582

  30. R.M. Smith, M.A. Arnold, Appl. Spectrosc. Rev. 46(8), 636 (2011). https://doi.org/10.1080/05704928.2011.614305

    Article  ADS  Google Scholar 

  31. N.P. Armitage, Electrodynamics of correlated electron systems (2018)

  32. R. Kubo, J. Phys. Soc. Jpn. 12(6), 570 (1957). https://doi.org/10.1143/JPSJ.12.570

    Article  ADS  Google Scholar 

  33. P.B. Allen, Phys. Rev. B 3, 305 (1971). https://doi.org/10.1103/PhysRevB.3.305

    Article  ADS  Google Scholar 

  34. J.W. Allen, J.C. Mikkelsen, Phys. Rev. B 15, 2952 (1977). https://doi.org/10.1103/PhysRevB.15.2952

    Article  ADS  Google Scholar 

  35. N. Smith, Phys. Rev. B 64(2001). https://doi.org/10.1103/PhysRevB.64.155106

  36. S.J. Youn, T.H. Rho, B.I. Min, K.S. Kim, Phys. Status Solidi (b) 244(4), 1354 (2007).https://doi.org/10.1002/pssb.200642097

  37. L. Wu, W.K. Tse, M. Brahlek, C.M. Morris, R.V. Aguilar, N. Koirala, S. Oh, N.P. Armitage, Phys. Rev. Lett. 115, 217602 (2015). https://doi.org/10.1103/PhysRevLett.115.217602

    Article  ADS  Google Scholar 

  38. E. Hendry, M. Koeberg, B. O’Regan, M. Bonn, Nano Lett. 6(4), 755 (2006). https://doi.org/10.1021/nl0600225

    Article  ADS  Google Scholar 

  39. M. Kaushik, B.W.H. Ng, B.M. Fischer, D. Abbott, Appl. Phys. Lett. 100(1), 011107 (2012). https://doi.org/10.1063/1.3674289

    Article  ADS  Google Scholar 

  40. M.H. Bergen, J. Reich, T. Ho, F. Clark, M. Reid, J.F. Holzman, Appl. Phys. Lett. 115(4), 041901 (2019). https://doi.org/10.1063/1.5101068

    Article  ADS  Google Scholar 

  41. G. Duan, J. Schalch, X. Zhao, A. Li, C. Chen, R.D. Averitt, X. Zhang, Sens. Actuators A Phys. 287, 21 (2019). https://doi.org/10.1016/j.sna.2018.12.039. https://www.sciencedirect.com/science/article/pii/S0924424718317278

  42. F. Garet, M. Hofman, J. Meilhan, F. Simoens, J.L. Coutaz, Appl. Phys. Lett. 105(3), 031106 (2014). https://doi.org/10.1063/1.4890732

    Article  ADS  Google Scholar 

  43. K. Shimakawa, H. Naito, S. Kasap, Philos. Mag. Lett. 89(11), 673 (2009). https://doi.org/10.1080/09500830903240691

    Article  ADS  Google Scholar 

  44. E.P. Parrott, J.A. Zeitler, L.F. Gladden, Opt. Lett. 34(23), 3722 (2009). https://doi.org/10.1364/OL.34.003722. http://ol.osa.org/abstract.cfm?URI=ol-34-23-3722

  45. P. Kužel, H. Němec, J. Phys. D Appl. Phys. 47(37), 374005 (2014). https://doi.org/10.1088/0022-3727/47/37/374005

    Article  Google Scholar 

  46. V.A. Markel, J. Opt. Soc. Am. A 33(7), 1244 (2016), https://doi.org/10.1364/JOSAA.33.001244. http://josaa.osa.org/abstract.cfm?URI=josaa-33-7-1244

  47. J.C. Dyre, Phys. Rev. B 48, 12511 (1993). https://doi.org/10.1103/PhysRevB.48.12511

    Article  ADS  Google Scholar 

  48. J.C. Dyre, T.B. Schrøder, Rev. Mod. Phys. 72, 873 (2000). https://doi.org/10.1103/RevModPhys.72.873

    Article  ADS  Google Scholar 

  49. D.G. Cooke, A.N. MacDonald, A. Hryciw, J. Wang, Q. Li, A. Meldrum, F.A. Hegmann, Phys. Rev. B 73, 193311 (2006). https://doi.org/10.1103/PhysRevB.73.193311

    Article  ADS  Google Scholar 

  50. J.B. Baxter, G.W. Guglietta, Anal. Chem. 83(12), 4342 (2011). https://doi.org/10.1021/ac200907z

    Article  Google Scholar 

  51. T.A. Liu, M. Tani, C.L. Pan, Journal of Applied Physics 93(5), 2996 (2003). https://doi.org/10.1063/1.1541105

    Article  ADS  Google Scholar 

  52. K. Yamamoto, H. Ishida, Vib. Spectrosc. 8(1), 1 (1994). https://doi.org/10.1016/0924-2031(94)00022-9. http://www.sciencedirect.com/science/article/pii/0924203194000229

  53. M. Tani, M. Herrmann, K. Sakai, Measur. Sci. Technol. 13(11), 1739 (2002). http://stacks.iop.org/0957-0233/13/i=11/a=310

  54. Y. Zhang, X. Zhang, S. Li, J. Gu, Y. Li, Z. Tian, C. Ouyang, M. He, J. Han, W. Zhang, Sci. Rep. 6(1), 26949 (2016). https://doi.org/10.1038/srep26949

    Article  ADS  Google Scholar 

  55. A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R.U.A. Khan, P. Gunter, J. Opt. Soc. Am. B Opt. Phys 23(9), 1822 (2006). https://doi.org/10.1364/JOSAB.23.001822

    Article  ADS  Google Scholar 

  56. M. Jazbinsek, U. Puc, A. Abina, A. Zidansek, Appl. Sci. Basel 9(5), 882 (2019). https://doi.org/10.3390/app9050882

    Article  Google Scholar 

  57. M.D. Thomson, V. Blank, H.G. Roskos, Opt. Express 18(22), 23173 (2010). https://doi.org/10.1364/OE.18.023173

    Article  ADS  Google Scholar 

  58. J.M. Dai, J. Liu, X.C. Zhang, IEEE J. Sel. Top. Quantum Electron. 17(1), 183 (2011). https://doi.org/10.1109/JSTQE.2010.2047007

    Article  ADS  Google Scholar 

  59. E. Matsubara, M. Nagai, M. Ashida, Appl. Phys. Lett. 101(1), 011105 (2012). https://doi.org/10.1063/1.4732524

    Article  ADS  Google Scholar 

  60. M. Tani, S. Matsuura, K. Sakai, S. ichi Nakashima, Appl. Opt. 36(30), 7853 (1997). https://doi.org/10.1364/AO.36.007853. http://ao.osa.org/abstract.cfm?URI=ao-36-30-7853

  61. K. Shimamura, B. Vidal, T. Nagatsuma, N.J. Gomes, T.E. Darcie, Adv. Opt. Technol. 2012, 925065 (2012). https://doi.org/10.1155/2012/925065

  62. F.C. De Lucia, J. Mol. Spectrosc. 261(1), 1 (2010). https://doi.org/10.1016/j.jms.2010.01.002. http://www.sciencedirect.com/science/article/pii/S0022285210000093

  63. L. Consolino, S. Bartalini, P. De Natale, J. Infrared Millim. Terahertz Waves 38(11), 1289 (2017). https://doi.org/10.1007/s10762-017-0406-x

  64. B.S. Williams, Nat. Photonics 1(9), 517 (2007). https://doi.org/10.1038/nphoton.2007.166

    Article  ADS  Google Scholar 

  65. K. Kawase, J. Shikata, H. Ito, J. Phys. D Appl. Phys. 35(3), PII (2002). https://doi.org/10.1088/0022-3727/35/3/201

  66. S. Suzuki, M. Asada, A. Teranishi, H. Sugiyama, H. Yokoyama, Appl. Phys. Lett. 97(24), 242102 (2010). https://doi.org/10.1063/1.3525834

    Article  ADS  Google Scholar 

  67. M. Tani, O. Morikawa, S. Matsuura, M. Hangyo, Semicond. Sci. Technol. 20(7), S151 (2005). https://doi.org/10.1088/0268-1242/20/7/005

    Article  ADS  Google Scholar 

  68. B. Gorshunov, A. Volkov, I. Spektor, A. Prokhorov, A. Mukhin, M. Dressel, S. Uchida, A. Loidl, Int. J. Infrared Millim. Waves 26(9), 1217 (2005). https://doi.org/10.1007/s10762-005-7600-y

  69. A.V. Pronin, Y.G. Goncharov, T. Fischer, J. Wosnitza, Rev. Sci. Instrum. 80(12), 123904 (2009). https://doi.org/10.1063/1.3271035

    Article  ADS  Google Scholar 

  70. G. Winnewisser, S. Belov, T. Klaus, R. Schieder, J. Mol. Spectrosc. 184(2), 468 (1997). https://doi.org/10.1006/jmsp.1997.7341. http://www.sciencedirect.com/science/article/pii/S0022285297973410

  71. G. Klapper, F. Lewen, R. Gendriesch, S.P. Belov, G. Winnewisser, J. Mol. Spectrosc. 201, 124 (2000)

    Article  ADS  Google Scholar 

  72. M. Mondal, D. Chaudhuri, M. Salehi, C. Wan, N. Laurita, B. Cheng, A.V. Stier, M.A. Quintero, J. Moon, D. Jain et al., Phys. Rev. B 98(12), 121106 (2018). https://doi.org/10.1103/PhysRevB.98.121106

    Article  ADS  Google Scholar 

  73. D.K. George, A.V. Stier, C.T. Ellis, B.D. McCombe, J. Černe, A.G. Markelz, J. Opt. Soc. Am. B 29(6), 1406 (2012). https://doi.org/10.1364/JOSAB.29.001406. http://josab.osa.org/abstract.cfm?URI=josab-29-6-1406

  74. C.M. Morris, R.V. Aguilar, A.V. Stier, N.P. Armitage, Opt. Express 20(11), 12303 (2012).https://doi.org/10.1364/OE.20.012303. http://www.opticsexpress.org/abstract.cfm?URI=oe-20-11-12303

  75. L. Wu, M. Salehi, N. Koirala, J. Moon, S. Oh, N.P. Armitage, Science 354(6316), 1124 (2016). https://doi.org/10.1126/science.aaf5541. http://science.sciencemag.org/content/354/6316/1124

  76. G.S. Jenkins, D.C. Schmadel, H.D. Drew, Rev. Sci. Instrum. 81(8), 083903 (2010). https://doi.org/10.1063/1.3480554

    Article  ADS  Google Scholar 

  77. G.S. Jenkins, A.B. Sushkov, D.C. Schmadel, N.P. Butch, P. Syers, J. Paglione, H.D. Drew, Phys. Rev. B 82, 125120 (2010). https://doi.org/10.1103/PhysRevB.82.125120

    Article  ADS  Google Scholar 

  78. M.C. Beard, C.A. Schmuttenmaer, J. Chem. Phys. 114(7), 2903 (2001). https://doi.org/10.1063/1.1338526

    Article  ADS  Google Scholar 

  79. P. Han, X. Wang, Y. Zhang, Adv. Opt. Mater. 8(3), 1900533 (2020). https://doi.org/10.1002/adom.201900533

    Article  Google Scholar 

  80. K. Ohta, S. Tokonami, K. Takahashi, Y. Tamura, H. Yamada, K. Tominaga, J. Phys. Chem. B 121(43), 10157 (2017). https://doi.org/10.1021/acs.jpcb.7b07025

    Article  Google Scholar 

  81. D. Grischkowsky, S. Keiding, M. van Exter, C. Fattinger, J. Opt. Soc. Am. B 7(10), 2006 (1990). https://doi.org/10.1364/JOSAB.7.002006. http://josab.osa.org/abstract.cfm?URI=josab-7-10-2006

  82. M. van Exter, D. Grischkowsky, Phys. Rev. B 41, 12140 (1990). https://doi.org/10.1103/PhysRevB.41.12140. https://link.aps.org/doi/10.1103/PhysRevB.41.12140

  83. M. Tinkham, Introduction to Superconductivity, 2nd edn. (McGraw-Hill, New York, 1996)

  84. J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 106, 162 (1957). https://doi.org/10.1103/PhysRev.106.162

    Article  ADS  MathSciNet  Google Scholar 

  85. J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 108, 1175 (1957). https://doi.org/10.1103/PhysRev.108.1175

    Article  ADS  MathSciNet  Google Scholar 

  86. D.C. Mattis, J. Bardeen, Phys. Rev. 111, 412 (1958). https://doi.org/10.1103/PhysRev.111.412

    Article  ADS  Google Scholar 

  87. M. Beck, M. Klammer, S. Lang, P. Leiderer, V.V. Kabanov, G.N. Gol’tsman, J. Demsar, Phys. Rev. Lett. 107, 177007 (2011). https://doi.org/10.1103/PhysRevLett.107.177007

    Article  ADS  Google Scholar 

  88. A.V. Pronin, M. Dressel, A. Pimenov, A. Loidl, I.V. Roshchin, L.H. Greene, Phys. Rev. B 57, 14416 (1998). https://doi.org/10.1103/PhysRevB.57.14416

    Article  ADS  Google Scholar 

  89. M. Dressel, N. Drichko, B. Gorshunov, A. Pimenov, IEEE J. Sel. Top. Quantum Electron. 14(2), 399 (2008). https://doi.org/10.1109/JSTQE.2007.910764

    Article  ADS  Google Scholar 

  90. N. Bachar, U.S. Pracht, E. Farber, M. Dressel, G. Deutscher, M. Scheffler, J. Low Temp. Phys. 179(1–2), 83 (2015). https://doi.org/10.1007/s10909-014-1244-z

    Article  ADS  Google Scholar 

  91. U.S. Pracht, E. Heintze, C. Clauss, D. Hafner, R. Bek, D. Werner, S. Gelhorn, M. Scheffler, M. Dressel, D. Sherman, B. Gorshunov, K.S. Il’in, D. Henrich, M. Siegel, IEEE Trans. Terahertz Sci. Technol. 3(3), 269 (2013). https://doi.org/10.1109/TTHZ.2013.2255047

    Article  ADS  Google Scholar 

  92. U.S. Pracht, M. Scheffler, M. Dressel, D.F. Kalok, C. Strunk, T.I. Baturina, Phys. Rev. B 86, 184503 (2012). https://doi.org/10.1103/PhysRevB.86.184503

    Article  ADS  Google Scholar 

  93. J. Simmendinger, U.S. Pracht, L. Daschke, T. Proslier, J.A. Klug, M. Dressel, M. Scheffler, Phys. Rev. B 94(6), 064506 (2016). https://doi.org/10.1103/PhysRevB.94.064506

    Article  ADS  Google Scholar 

  94. R.A. Kaindl, M.A. Carnahan, J. Orenstein, D.S. Chemla, H.M. Christen, H.Y. Zhai, M. Paranthaman, D.H. Lowndes, Phys. Rev. Lett. 88, 027003 (2001). https://doi.org/10.1103/PhysRevLett.88.027003

    Article  ADS  Google Scholar 

  95. M. Mondal, A. Kamlapure, M. Chand, G. Saraswat, S. Kumar, J. Jesudasan, L. Benfatto, V. Tripathi, P. Raychaudhuri, Phys. Rev. Lett. 106, 047001 (2011). https://doi.org/10.1103/PhysRevLett.106.047001

    Article  ADS  Google Scholar 

  96. M. Mondal, S. Kumar, M. Chand, A. Kamlapure, G. Saraswat, G. Seibold, L. Benfatto, P. Raychaudhuri, Phys. Rev. Lett. 107, 21 (2011). https://doi.org/10.1103/physrevlett.107.217003

    Article  Google Scholar 

  97. D. Sherman, B. Gorshunov, S. Poran, N. Trivedi, E. Farber, M. Dressel, A. Frydman, Phys. Rev. B 89, 035149 (2014). https://doi.org/10.1103/PhysRevB.89.035149

    Article  ADS  Google Scholar 

  98. C. Renner, B. Revaz, J.Y. Genoud, K. Kadowaki, O. Fischer, Phys. Rev. Lett. 80(1), 149 (1998). https://doi.org/10.1103/PhysRevLett.80.149

    Article  ADS  Google Scholar 

  99. T. Timusk, B. Statt, Rep. Progr. Phys. 62(1), 61 (1999). https://doi.org/10.1088/0034-4885/62/1/002

    Article  ADS  Google Scholar 

  100. B. Sacépé, C. Chapelier, T.I. Baturina, V.M. Vinokur, M.R. Baklanov, M. Sanquer, Nat. Commun. 1(1), 140 (2010). https://doi.org/10.1038/ncomms1140

    Article  Google Scholar 

  101. B. Sacépé, T. Dubouchet, C. Chapelier, M. Sanquer, M. Ovadia, D. Shahar, M. Feigel’man, L. Ioffe, Nat. Phys. 7(3), 239 (2011). https://doi.org/10.1038/nphys1892

    Article  Google Scholar 

  102. M. Chand, G. Saraswat, A. Kamlapure, M. Mondal, S. Kumar, J. Jesudasan, V. Bagwe, L. Benfatto, V. Tripathi, P. Raychaudhuri, Phys. Rev. B 85, 014508 (2012). https://doi.org/10.1103/PhysRevB.85.014508

    Article  ADS  Google Scholar 

  103. D. Sherman, U.S. Pracht, B. Gorshunov, S. Poran, J. Jesudasan, M. Chand, P. Raychaudhuri, M. Swanson, N. Trivedi, A. Auerbach, M. Scheffler, A. Frydman, M. Dressel, Nat. Phys. 11(2), 188 (2015). https://doi.org/10.1038/nphys3227

    Article  Google Scholar 

  104. S.C. et. al., Phys. Lett. B 716(1), 30 (2012). https://doi.org/10.1016/j.physletb.2012.08.021. http://www.sciencedirect.com/science/article/pii/S0370269312008581

  105. G. Aad et al., Phys. Lett. B 716(1), 1 (2012). https://doi.org/10.1016/j.physletb.2012.08.020. http://www.sciencedirect.com/science/article/pii/S037026931200857X

  106. M. Spira, A. Djouadi, D. Graudenz, R. Zerwas, Nucl. Phys. B 453(1), 17 (1995). https://doi.org/10.1016/0550-3213(95)00379-7. http://www.sciencedirect.com/science/article/pii/0550321395003797

  107. M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schaub, C. Gross, E. Demler, S. Kuhr, I. Bloch, Nature 487(7408), 454 (2012). https://doi.org/10.1038/nature11255

  108. P.B. Littlewood, C.M. Varma, Phys. Rev. B 26, 4883 (1982). https://doi.org/10.1103/PhysRevB.26.4883

    Article  ADS  Google Scholar 

  109. G.M. Luke, Y. Fudamoto, K.M. Kojima, M.I. Larkin, J. Merrin, B. Nachumi, Y.J. Uemura, Y. Maeno, Z.Q. Mao, Y. Mori, H. Nakamura, M. Sigrist, Nature 394(6693), 558 (1998). https://doi.org/10.1038/29038

    Article  ADS  Google Scholar 

  110. A.J. Leggett, F. Sols, Found. Phys. 21(3), 353 (1991). https://doi.org/10.1007/BF01883640

    Article  ADS  Google Scholar 

  111. D.J. Gross, Proc. Natl. Acad. Sci. 93(25), 14256 (1996). https://doi.org/10.1073/pnas.93.25.14256

    Article  ADS  Google Scholar 

  112. P.I. Hurtado, C. Pérez-Espigares, J.J. del Pozo, P.L. Garrido, Proc. Natl. Acad. Sci. 108(19), 7704 (2011). https://doi.org/10.1073/pnas.1013209108. https://www.pnas.org/content/108/19/7704

  113. R. Matsunaga, Y.I. Hamada, K. Makise, Y. Uzawa, H. Terai, Z. Wang, R. Shimano, Phys. Rev. Lett. 111, 057002 (2013). https://doi.org/10.1103/PhysRevLett.111.057002

    Article  ADS  Google Scholar 

  114. R. Matsunaga, N. Tsuji, H. Fujita, A. Sugioka, K. Makise, Y. Uzawa, H. Terai, Z. Wang, H. Aoki, R. Shimano, Science 345(6201), 1145 (2014). https://doi.org/10.1126/science.1254697. http://science.sciencemag.org/content/345/6201/1145

  115. P. Merchant, B. Normand, K.W. Krämer, M. Boehm, D.F. McMorrow, C. Rüegg, Nat. Phys. 10(5), 373 (2014). https://doi.org/10.1038/nphys2902

  116. T. Hong, M. Matsumoto, Y. Qiu, W. Chen, T.R. Gentile, S. Watson, F.F. Awwadi, M.M. Turnbull, S.E. Dissanayake, H. Agrawal, R. Toft-Petersen, B. Klemke, K. Coester, K.P. Schmidt, D.A. Tennant, Nat. Phys. 13(7), 638 (2017). https://doi.org/10.1038/nphys4182

  117. A. Jain, M. Krautloher, J. Porras, G. Ryu, D. Chen, D. Abernathy, J. Park, A. Ivanov, J. Chaloupka, G. Khaliullin, B. Keimer, B. Kim, Nat. Phys. 13(7), 633 (2017). https://doi.org/10.1038/nphys4077

  118. U. Bissbort, S. Götze, Y. Li, J. Heinze, J.S. Krauser, M. Weinberg, C. Becker, K. Sengstock, W. Hofstetter, Phys. Rev. Lett. 106, 205303 (2011). https://doi.org/10.1103/PhysRevLett.106.205303

    Article  ADS  Google Scholar 

  119. T. Cea, D. Bucheli, G. Seibold, L. Benfatto, J. Lorenzana, C. Castellani, Phys. Rev. B 89, 174506 (2014). https://doi.org/10.1103/PhysRevB.89.174506

    Article  ADS  Google Scholar 

  120. T. Cea, L. Benfatto, Phys. Rev. B 90, 224515 (2014). https://doi.org/10.1103/PhysRevB.90.224515

    Article  ADS  Google Scholar 

  121. M.A. Méasson, Y. Gallais, M. Cazayous, B. Clair, P. Rodière, L. Cario, A. Sacuto, Phys. Rev. B 89, 060503 (2014). https://doi.org/10.1103/PhysRevB.89.060503

    Article  ADS  Google Scholar 

  122. R. Matsunaga, N. Tsuji, K. Makise, H. Terai, H. Aoki, R. Shimano, Phys. Rev. B 96, 020505 (2017). https://doi.org/10.1103/PhysRevB.96.020505

    Article  ADS  Google Scholar 

  123. B. Cheng, L. Wu, N.J. Laurita, H. Singh, M. Chand, P. Raychaudhuri, N.P. Armitage, Phys. Rev. B 93, 180511 (2016). https://doi.org/10.1103/PhysRevB.93.180511

    Article  ADS  Google Scholar 

  124. L.S. Bilbro, R.V. Aguilar, G. Logvenov, O. Pelleg, I. Bozovic, N.P. Armitage, Nat. Phys. 7(4), 298 (2011). https://doi.org/10.1038/NPHYS1912

    Article  Google Scholar 

  125. V.J. Emery, S.A. Kivelson, Nature 374(6521), 434 (1995). https://doi.org/10.1038/374434a0

  126. F. Mahmood, X. He, I. Bozovic, N.P. Armitage, Phys. Rev. Lett. 122(2), 027003 (2019). https://doi.org/10.1103/PhysRevLett.122.027003

    Article  ADS  Google Scholar 

  127. A. Kamlapure, M. Mondal, M. Chand, A. Mishra, J. Jesudasan, V. Bagwe, L. Benfatto, V. Tripathi, P. Raychaudhuri, Appl. Phys. Lett. 96(7), 072509 (2010). https://doi.org/10.1063/1.3314308

    Article  ADS  Google Scholar 

  128. K. Yamaguchi, T. Kurihara, Y. Minami, M. Nakajima, T. Suemoto, Phys. Rev. Lett. 110, 137204 (2013). https://doi.org/10.1103/PhysRevLett.110.137204

    Article  ADS  Google Scholar 

  129. T.J. Huisman, R.V. Mikhaylovskiy, A.V. Telegin, Y.P. Sukhorukov, A.B. Granovsky, S.V. Naumov, T. Rasing, A.V. Kimel, Appl. Phys. Lett. 106(13), 132411 (2015). https://doi.org/10.1063/1.4916884

    Article  ADS  Google Scholar 

  130. P. Chauhan, F. Mahmood, H.J. Changlani, S.M. Koohpayeh, N.P. Armitage, Phys. Rev. Lett. 124, 037203 (2020). https://doi.org/10.1103/PhysRevLett.124.037203

    Article  ADS  Google Scholar 

  131. P. Zhang, F. Su, X. Chen, S. Zhang, H. Mei, Z. Yang, J. Dai, L. Pi, Appl. Phys. Express 9(10), 102401 (2016). https://doi.org/10.7567/apex.9.102401

    Article  ADS  Google Scholar 

  132. K.E. Sickafus, J.M. Wills, N.W. Grimes, J. Am. Ceram. Soc. 82(12), 3279 (1999). https://doi.org/10.1111/j.1151-2916.1999.tb02241.x. https://ceramics.onlinelibrary.wiley.com/doi/abs/10.1111/j.1151-2916.1999.tb02241.x

  133. C. Biagioni, M. Pasero, Am. Mineral. 99(7), 1254 (2014). https://doi.org/10.2138/am.2014.4816

    Article  ADS  Google Scholar 

  134. W. Hu, N. Qin, G.H. Wu, Y.T. Lin, S.W. Li, D.H. Bao, J. Am. Chem. Soc. 134(36), 14658 (2012). https://doi.org/10.1021/ja305681n

    Article  Google Scholar 

  135. I. Ganesh, Int. Mater. Rev. 58(2), 63 (2013). https://doi.org/10.1179/1743280412Y.0000000001

    Article  ADS  Google Scholar 

  136. S.J. Peng, L.L. Li, Y.X. Hu, M. Srinivasan, F.Y. Cheng, J. Chen, S. Ramakrishna, ACS Nano 9(2), 1945 (2015). https://doi.org/10.1021/nn506851x

    Article  Google Scholar 

  137. J.H. Park, Metall. Mater. Trans. B 38(4), 657 (2007). https://doi.org/10.1007/s11663-007-9066-x

  138. Q. Zhao, Z.H. Yan, C.C. Chen, J. Chen, Chem. Rev. 117(15), 10121 (2017). https://doi.org/10.1021/acs.chemrev.7b00051

    Article  Google Scholar 

  139. Y. Huang, J. Yuan, K. Jin, W. Zhang, K. Reichel, D.M. Mittleman, 2018 Conference on Lasers and Electro-optics (CLEO) (IEEE, 2018)

  140. A.V. Kimel, A. Kirilyuk, A. Tsvetkov, R.V. Pisarev, T. Rasing, Nature 429(6994), 850 (2004). https://doi.org/10.1038/nature02659

  141. A.V. Kimel, A. Kirilyuk, P.A. Usachev, R.V. Pisarev, A.M. Balbashov, T. Rasing, Nature 435(7042), 655 (2005). https://doi.org/10.1038/nature03564

  142. A.V. Kimel, B.A. Ivanov, R.V. Pisarev, P.A. Usachev, A. Kirilyuk, T. Rasing, Nat. Phys. 5(10), 727 (2009). https://doi.org/10.1038/nphys1369

  143. N. Kanda, T. Higuchi, H. Shimizu, K. Konishi, K. Yoshioka, M. Kuwata-Gonokami, Nat. Commun. 2(1), 362 (2011). https://doi.org/10.1038/ncomms1366

  144. R. Iida, T. Satoh, T. Shimura, K. Kuroda, B.A. Ivanov, Y. Tokunaga, Y. Tokura, Phys. Rev. B 84, 064402 (2011). https://doi.org/10.1103/PhysRevB.84.064402

    Article  ADS  Google Scholar 

  145. J.A. de Jong, A.V. Kimel, R.V. Pisarev, A. Kirilyuk, T. Rasing, Phys. Rev. B 84, 104421 (2011). https://doi.org/10.1103/PhysRevB.84.104421

    Article  ADS  Google Scholar 

  146. J.A. de Jong, I. Razdolski, A.M. Kalashnikova, R.V. Pisarev, A.M. Balbashov, A. Kirilyuk, T. Rasing, A.V. Kimel, Phys. Rev. Lett. 108, 157601 (2012). https://doi.org/10.1103/PhysRevLett.108.157601

    Article  ADS  Google Scholar 

  147. J. Jiang, Z. Jin, G. Song, X. Lin, G. Ma, S. Cao, Appl. Phys. Lett. 103(6), 062403 (2013). https://doi.org/10.1063/1.4818135

    Article  ADS  Google Scholar 

  148. X.M. Liu, Z.M. Jin, S.N. Zhang, K.L. Zhang, W.Y. Zhao, K. Xu, X. Lin, Z.X. Cheng, S.X. Cao, G.H. Ma, J. Phys. D Appl. Phys. 51(2), 024001 (2018). https://doi.org/10.1088/1361-6463/aa9b5d

    Article  ADS  Google Scholar 

  149. X.Y. Zhao, K.L. Zhang, K. Xu, P.W. Man, T. Xie, A.H. Wu, G.H. Ma, S.X. Cao, L.B. Su, Solid State Commun. 231, 43 (2016). https://doi.org/10.1016/j.ssc.2016.02.002

    Article  ADS  Google Scholar 

  150. X. Liu, T. Xie, J. Guo, S. Yang, Y. Song, X. Lin, S. Cao, Z. Cheng, Z. Jin, A. Wu, G. Ma, J. Yao, Appl. Phys. Lett. 113(2), 022401 (2018). https://doi.org/10.1063/1.5037119

    Article  ADS  Google Scholar 

  151. X. Zeng, X. Fu, X. Xi, D. Wang, J. Zhou, B. Li, Mater. Lett. 164, 64 (2016). https://doi.org/10.1016/j.matlet.2015.10.115. http://www.sciencedirect.com/science/article/pii/S0167577X15307643

  152. E. Constable, D.L. Cortie, J. Horvat, R.A. Lewis, Z. Cheng, G. Deng, S. Cao, S. Yuan, G. Ma, Phys. Rev. B 90, 054413 (2014). https://doi.org/10.1103/PhysRevB.90.054413

    Article  ADS  Google Scholar 

  153. G. Song, J. Jiang, B. Kang, J. Zhang, Z. Cheng, G. Ma, S. Cao, Solid State Commun. 211, 47 (2015). https://doi.org/10.1016/j.ssc.2015.03.013. http://www.sciencedirect.com/science/article/pii/S0038109815001064

  154. R.V. Mikhaylovskiy, E. Hendry, V.V. Kruglyak, R.V. Pisarev, T. Rasing, A.V. Kimel, Phys. Rev. B 90, 184405 (2014). https://doi.org/10.1103/PhysRevB.90.184405

    Article  ADS  Google Scholar 

  155. T. Suemoto, K. Nakamura, T. Kurihara, H. Watanabe, Appl. Phys. Lett. 107(4), 042404 (2015). https://doi.org/10.1063/1.4927431

    Article  ADS  Google Scholar 

  156. X. Lin, J. Jiang, Z. Jin, D. Wang, Z. Tian, J. Han, Z. Cheng, G. Ma, Appl. Phys. Lett. 106(9), 092403 (2015). https://doi.org/10.1063/1.4913998

    Article  ADS  Google Scholar 

  157. X. Li, M. Bamba, N. Yuan, Q. Zhang, Y. Zhao, M. Xiang, K. Xu, Z. Jin, W. Ren, G. Ma, S. Cao, D. Turchinovich, J. Kono, Science 361(6404), 794 (2018). https://doi.org/10.1126/science.aat5162. https://science.sciencemag.org/content/361/6404/794

  158. M. Gross, S. Haroche, Phys. Rep. 93(5), 301 (1982). https://doi.org/10.1016/0370-1573(82)90102-8. http://www.sciencedirect.com/science/article/pii/0370157382901028

  159. E. Ising, Z. für Phys. 31(1), 253 (1925). https://doi.org/10.1007/BF02980577

  160. H. Bethe, Z. für Phys. 71(3), 205 (1931). https://doi.org/10.1007/BF01341708

  161. P.W. Anderson, Phys. Rev. 86, 694 (1952). https://doi.org/10.1103/PhysRev.86.694

    Article  ADS  Google Scholar 

  162. R. Kubo, Phys. Rev. 87, 568 (1952). https://doi.org/10.1103/PhysRev.87.568

    Article  ADS  Google Scholar 

  163. L. Faddeev, L. Takhtajan, Phys. Lett. A 85(6), 375 (1981). https://doi.org/10.1016/0375-9601(81)90335-2. http://www.sciencedirect.com/science/article/pii/0375960181903352

  164. I. Affleck, J. Phys. Condens. Matter 1(19), 3047 (1989). https://doi.org/10.1088/0953-8984/1/19/001

    Article  ADS  Google Scholar 

  165. F.D.M. Haldane, Phys. Rev. Lett. 50, 1153 (1983). https://doi.org/10.1103/PhysRevLett.50.1153

    Article  ADS  MathSciNet  Google Scholar 

  166. R. Coldea, D.A. Tennant, E.M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, K. Kiefer, Science 327(5962), 177 (2010). https://doi.org/10.1126/science.1180085. https://science.sciencemag.org/content/327/5962/177

  167. A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 416(6881), 608 (2002). https://doi.org/10.1038/416608a

    Article  ADS  Google Scholar 

  168. N. Blanc, J. Trinh, L. Dong, X. Bai, A.A. Aczel, M. Mourigal, L. Balents, T. Siegrist, A.P. Ramirez, Nat. Phys. 14(3), 273 (2018). https://doi.org/10.1038/s41567-017-0010-y

  169. K.S. Novoselov, Rev. Mod. Phys. 83, 837 (2011). https://doi.org/10.1103/RevModPhys.83.837

    Article  ADS  Google Scholar 

  170. F. Bonaccorso, L. Colombo, G. Yu, M. Stoller, V. Tozzini, A.C. Ferrari, R.S. Ruoff, V. Pellegrini, Science 347, 1246501 (2015)

  171. S.Z. Butler, S.M. Hollen, L. Cao, Y. Cui, J.A. Gupta, H.R. Gutiérrez, T.F. Heinz, S.S. Hong, J. Huang, A.F. Ismach, E. Johnston-Halperin, M. Kuno, V.V. Plashnitsa, R.D. Robinson, R.S. Ruoff, S. Salahuddin, J. Shan, L. Shi, M.G. Spencer, M. Terrones, W. Windl, J.E. Goldberger, ACS Nano 7(4), 2898 (2013). https://doi.org/10.1021/nn400280c

    Article  Google Scholar 

  172. C.M. Morris, R. Valdés Aguilar, A. Ghosh, S.M. Koohpayeh, J. Krizan, R.J. Cava, O. Tchernyshyov, T.M. McQueen, N.P. Armitage, Phys. Rev. Lett. 112, 137403 (2014). https://doi.org/10.1103/PhysRevLett.112.137403. https://link.aps.org/doi/10.1103/PhysRevLett.112.137403

  173. K. Amelin, J. Engelmayer, J. Viirok, U. Nagel, T. Rõ om, T. Lorenz, Z. Wang, Phys. Rev. B 102, 104431 (2020). https://doi.org/10.1103/PhysRevB.102.104431. https://link.aps.org/doi/10.1103/PhysRevB.102.104431

  174. K.S. Burch, D. Mandrus, J.G. Park, Nature 563(7729), 47 (2018). https://doi.org/10.1038/s41586-018-0631-z

    Article  ADS  Google Scholar 

  175. J.U. Lee, S. Lee, J.H. Ryoo, S. Kang, T.Y. Kim, P. Kim, C.H. Park, J.G. Park, H. Cheong, Nano Lett. 16(12), 7433 (2016). https://doi.org/10.1021/acs.nanolett.6b03052

    Article  ADS  Google Scholar 

  176. X. Wang, K. Du, Y.Y.F. Liu, P. Hu, J. Zhang, Q. Zhang, M.H.S. Owen, X. Lu, C.K. Gan, P. Sengupta, C. Kloc, Q. Xiong, 2D Materials 3(3), 031009 (2016). https://doi.org/10.1088/2053-1583/3/3/031009. https://doi.org/10.1088%2F2053-1583%2F3%2F3%2F031009

  177. B. Huang, G. Clark, E. Navarro-Moratalla, D.R. Klein, R. Cheng, K.L. Seyler, D. Zhong, E. Schmidgall, M.A. McGuire, D.H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391

  178. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z.Q. Qiu, R.J. Cava, S.G. Louie, J. Xia, X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060

  179. M. Bonilla, S. Kolekar, Y. Ma, H.C. Diaz, V. Kalappattil, R. Das, T. Eggers, H.R. Gutierrez, M.H. Phan, M. Batzill, Nat. Nanotechnol.13(4), 289 (2018). https://doi.org/10.1038/s41565-018-0063-9

  180. D. O’Hara, T. Zhu, A.H. Trout, A.S. Ahmed, Y.K. Luo, C.H. Lee, M.R. Brenner, S. Rajan, J.A. Gupta, D.W. McComb, R.K. Kawakami, Nano Lett. 18(5), 3125 (2018). https://doi.org/10.1021/acs.nanolett.8b00683

    Article  ADS  Google Scholar 

  181. J.M. Kosterlitz, J. Phys. C Solid State Phys. 7(6), 1046 (1974). https://doi.org/10.1088/0022-3719/7/6/005

    Article  ADS  Google Scholar 

  182. J.M. Kosterlitz, D.J. Thouless, J. Phys. C Solid State Phys. 6(7), 1181 (1973). https://doi.org/10.1088/0022-3719/6/7/010

    Article  ADS  Google Scholar 

  183. Z. Wang, M. Schmidt, A. Loidl, J. Wu, H. Zou, W. Yang, C. Dong, Y. Kohama, K. Kindo, D.I. Gorbunov, S. Niesen, O. Breunig, J. Engelmayer, T. Lorenz, Phys. Rev. Lett. 123, 067202 (2019). https://doi.org/10.1103/PhysRevLett.123.067202

    Article  ADS  Google Scholar 

  184. S. Kimura, H. Yashiro, K. Okunishi, M. Hagiwara, Z. He, K. Kindo, T. Taniyama, M. Itoh, Phys. Rev. Lett. 99, 087602 (2007). https://doi.org/10.1103/PhysRevLett.99.087602

    Article  ADS  Google Scholar 

  185. Q. Faure, S. Takayoshi, V. Simonet, B. Grenier, M. Månsson, J.S. White, G.S. Tucker, C. Rüegg, P. Lejay, T. Giamarchi, S. Petit, Phys. Rev. Lett. 123, 027204 (2019). https://doi.org/10.1103/PhysRevLett.123.027204

    Article  ADS  Google Scholar 

  186. Z. Zhang, K. Amelin, X. Wang, H. Zou, J. Yang, U. Nagel, T. Rõ om, T. Dey, A.A. Nugroho, T. Lorenz, J. Wu, Z. Wang, Phys. Rev. B 101, 220411 (2020). https://doi.org/10.1103/PhysRevB.101.220411

  187. L. Balents, Nature 464, 199 (2010). http://www.nature.com/nature/journal/v464/n7286/abs/nature08917.html

  188. Z. Wang, S. Reschke, D. Hüvonen, S.H. Do, K. Choi, M. Gensch, U. Nage, T. Rõõm, A. Loidl, Phys. Rev. Lett. 119 (2017). https://doi.org/10.1103/PhysRevLett.119.227202

  189. S. Reschke, F. Mayr, S. Widmann, H.A.K. von Niddal, V. Tsurkan, M.V. Eremin, S.H. Do, K.Y. Choi, Z. Wang, A. Loidl, J. Phys. Condens. Matter 30(47), 475604 (2018). https://doi.org/10.1088/1361-648X/aae805

    Article  Google Scholar 

  190. L. Wu, A. Little, E.E. Aldape, D. Rees, E. Thewalt, P. Lampen-Kelley, A. Banerjee, C.A. Bridges, J.Q. Yan, D. Boone, S. Patankar, D. Goldhaber-Gordon, D. Mandrus, S.E. Nagler, E. Altman, J. Orenstein, Phys. Rev. B 98, 094425 (2018). https://doi.org/10.1103/PhysRevB.98.094425

    Article  ADS  Google Scholar 

  191. L.Y. Shi, Y.Q. Liu, T. Lin, M.Y. Zhang, S.J. Zhang, L. Wang, Y.G. Shi, T. Dong, N.L. Wang, Phys. Rev. B 98, 094414 (2018). https://doi.org/10.1103/PhysRevB.98.094414

    Article  ADS  Google Scholar 

  192. C. Wellm, J. Zeisner, A. Alfonsov, A.U.B. Wolter, M. Roslova, A. Isaeva, T. Doert, M. Vojta, B. Büchner, V. Kataev, Phys. Rev. B 98, 184408 (2018). https://doi.org/10.1103/PhysRevB.98.184408

    Article  ADS  Google Scholar 

  193. A. Sahasrabudhe, D.A.S. Kaib, S. Reschke, R. German, T.C. Koethe, J. Buhot, D. Kamenskyi, C. Hickey, P. Becker, V. Tsurkan, A. Loidl, S.H. Do, K.Y. Choi, M. Grüninger, S.M. Winter, Z. Wang, R. Valentí, P.H.M. van Loosdrecht, Phys. Rev. B 101, 140410 (2020). https://doi.org/10.1103/PhysRevB.101.140410

    Article  ADS  Google Scholar 

  194. M. Majumder, M. Prinz-Zwick, S. Reschke, A. Zubtsovskii, T. Dey, F. Freund, N. Büttgen, A. Jesche, I. Kézsmárki, A.A. Tsirlin, P. Gegenwart, Phys. Rev. B 101, 214417 (2020). https://doi.org/10.1103/PhysRevB.101.214417

    Article  ADS  Google Scholar 

  195. X. Fu, X. Zeng, D. Wang, H. C. Zhang, J. Han, T.J. Cui, Sci. Rep. 5(1), 14777 (2015). https://doi.org/10.1038/srep14777

  196. G.A. Khodaparast, D.C. Larrabee, J. Kono, D.S. King, J. Kato, T. Slupinski, A. Oiwa, H. Munekata, G.D. Sanders, C.J. Stanton, J. Appl. Phys. 93(10), 8286 (2003). https://doi.org/10.1063/1.1555375

    Article  ADS  Google Scholar 

  197. L. Wu, M. Brahlek, R. Valdes Aguilar, A.V. Stier, C.M. Morris, Y. Lubashevsky, L.S. Bilbro, N. Bansal, S. Oh, N.P. Armitage, Nat. Phys. 9(7), 410 (2013). https://doi.org/10.1038/nphys2647

  198. J.E. Moore, Nature 464(7286), 194 (2010). https://doi.org/10.1038/nature08916

  199. M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010). https://doi.org/10.1103/RevModPhys.82.3045

    Article  ADS  Google Scholar 

  200. X.L. Qi, S.C. Zhang, Rev. Mod. Phys. 83, 1057 (2011). https://doi.org/10.1103/RevModPhys.83.1057

    Article  ADS  Google Scholar 

  201. L. Fu, C.L. Kane, E.J. Mele, Phys. Rev. Lett. 98, 106803 (2007). https://doi.org/10.1103/PhysRevLett.98.106803

    Article  ADS  Google Scholar 

  202. C.K. Chiu, J.C.Y. Teo, A.P. Schnyder, S. Ryu, Rev. Mod. Phys. 88, 035005 (2016). https://doi.org/10.1103/RevModPhys.88.035005

    Article  ADS  Google Scholar 

  203. S. Rachel, Rep. Progr. Phys. 81(11), 116501 (2018). https://doi.org/10.1088/1361-6633/aad6a6

    Article  ADS  Google Scholar 

  204. A. Bansil, H. Lin, T. Das, Rev. Mod. Phys. 88, 021004 (2016). https://doi.org/10.1103/RevModPhys.88.021004

    Article  ADS  Google Scholar 

  205. M.G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B.A. Bernevig, Z. Wang, Nature 566(7745), 480 (2019). https://doi.org/10.1038/s41586-019-0954-4

  206. D. Hsieh, Y. Xia, D. Qian, L. Wray, J.H. Dil, F. Meier, J. Osterwalder, L. Patthey, J.G. Checkelsky, N.P. Ong, A.V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nature 460(7259), 1101 (2009). https://doi.org/10.1038/nature08234

    Article  ADS  Google Scholar 

  207. X.L. Qi, T.L. Hughes, S.C. Zhang, Phys. Rev. B 78, 195424 (2008). https://doi.org/10.1103/PhysRevB.78.195424

    Article  ADS  Google Scholar 

  208. X.L. Qi, R. Li, J. Zang, S.C. Zhang, Science 323(5918), 1184 (2009). https://doi.org/10.1126/science.1167747. http://science.sciencemag.org/content/323/5918/1184

  209. A.M. Essin, J.E. Moore, D. Vanderbilt, Phys. Rev. Lett. 102, 146805 (2009). https://doi.org/10.1103/PhysRevLett.102.146805

    Article  ADS  Google Scholar 

  210. K.N. Okada, Y. Takahashi, M. Mogi, R. Yoshimi, A. Tsukazaki, K.S. Takahashi, N. Ogawa, M. Kawasaki, Y. Tokura, Nat. Communic. 7(1), 12245 (2016). https://doi.org/10.1038/ncomms12245

  211. V. Dziom, A. Shuvaev, A. Pimenov, G.V. Astakhov, C. Ames, K. Bendias, J. Böttcher, G. Tkachov, E.M. Hankiewicz, C. Brüne, H. Buhmann, L.W. Molenkamp, Nat. Commun. 8(1), 15197 (2017). https://doi.org/10.1038/ncomms15197

  212. S. Souma, M. Komatsu, M. Nomura, T. Sato, A. Takayama, T. Takahashi, K. Eto, K. Segawa, Y. Ando, Phys. Rev. Lett. 109, 186804 (2012). https://doi.org/10.1103/PhysRevLett.109.186804

    Article  ADS  Google Scholar 

  213. T.H. O’Dell, Philos. Mag. J. Theor. Exp. Appl. Phys. 7(82), 1653 (1962). https://doi.org/10.1080/14786436208213701

    Article  Google Scholar 

  214. M. Fiebig, J. Phys. D Appl. Phys. 38(8), R123 (2005). https://doi.org/10.1088/0022-3727/38/8/r01

    Article  ADS  Google Scholar 

  215. W.K. Tse, A.H. MacDonald, Phys. Rev. Lett. 105, 057401 (2010). https://doi.org/10.1103/PhysRevLett.105.057401

    Article  ADS  Google Scholar 

  216. J. Maciejko, X.L. Qi, H.D. Drew, S.C. Zhang, Phys. Rev. Lett. 105, 166803 (2010). https://doi.org/10.1103/PhysRevLett.105.166803

    Article  ADS  Google Scholar 

  217. A.M. Shuvaev, G.V. Astakhov, G. Tkachov, C. Brüne, H. Buhmann, L.W. Molenkamp, A. Pimenov, Phys. Rev. B 87, 121104 (2013). https://doi.org/10.1103/PhysRevB.87.121104

    Article  ADS  Google Scholar 

  218. C. Brüne, C.X. Liu, E.G. Novik, E.M. Hankiewicz, H. Buhmann, Y.L. Chen, X.L. Qi, Z.X. Shen, S.C. Zhang, L.W. Molenkamp, Phys. Rev. Lett. 106, 126803 (2011). https://doi.org/10.1103/PhysRevLett.106.126803

    Article  ADS  Google Scholar 

  219. X. Li, K. Yoshioka, M. Xie, G.T. Noe, W. Lee, N. Marquez Peraca, W. Gao, T. Hagiwara, O.S. Handegård, L.W. Nien, T. Nagao, M. Kitajima, H. Nojiri, C.K. Shih, A.H. MacDonald, I. Katayama, J. Takeda, G.A. Fiete, J. Kono, Phys. Rev. B 100, 115145 (2019). https://doi.org/10.1103/PhysRevB.100.115145. https://link.aps.org/doi/10.1103/PhysRevB.100.115145

  220. X. Wan, A.M. Turner, A. Vishwanath, S.Y. Savrasov, Phys. Rev. B 83, 205101 (2011). https://doi.org/10.1103/PhysRevB.83.205101

    Article  ADS  Google Scholar 

  221. Z. Wang, Y. Sun, X.Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, Z. Fang, Phys. Rev. B 85, 195320 (2012). https://doi.org/10.1103/PhysRevB.85.195320

    Article  ADS  Google Scholar 

  222. Z. Wang, H. Weng, Q. Wu, X. Dai, Z. Fang, Phys. Rev. B 88, 125427 (2013). https://doi.org/10.1103/PhysRevB.88.125427

    Article  ADS  Google Scholar 

  223. M. Kargarian, M. Randeria, N. Trivedi, Sci. Rep. 5(1), 12683 (2015). https://doi.org/10.1038/srep12683

  224. I. Crassee, R. Sankar, W.L. Lee, A. Akrap, M. Orlita, Phys. Rev. Mater. 2, 120302 (2018). https://doi.org/10.1103/PhysRevMaterials.2.120302. https://link.aps.org/doi/10.1103/PhysRevMaterials.2.120302

  225. W. Lu, J. Ling, F. Xiu, D. Sun, Phys. Rev. B 98, 104310 (2018). https://doi.org/10.1103/PhysRevB.98.104310

    Article  ADS  Google Scholar 

  226. S. Kovalev, R.M.A. Dantas, S. Germanskiy, J.C. Deinert, B. Green, I. Ilyakov, N. Awari, M. Chen, M. Bawatna, J. Ling, F. Xiu, P.H.M. van Loosdrecht, P. Surówka, T. Oka, Z. Wang, Nat. Commun. 11(1), 2451 (2020). https://doi.org/10.1038/s41467-020-16133-8

  227. W. Zhang, Y. Yang, P. Suo, W. Zhao, J. Guo, Q. Lu, X. Lin, Z. Jin, L. Wang, G. Chen, F. Xiu, W. Liu, C. Zhang, G. Ma, Appl. Phys. Lett. 114(22), 221102 (2019). https://doi.org/10.1063/1.5086085

    Article  ADS  Google Scholar 

  228. B. Cheng, N. Kanda, T.N. Ikeda, T. Matsuda, P. Xia, T. Schumann, S. Stemmer, J. Itatani, N.P. Armitage, R. Matsunaga, Phys. Rev. Lett. 124, 117402 (2020). https://doi.org/10.1103/PhysRevLett.124.117402

    Article  ADS  Google Scholar 

  229. S.Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.C. Lee, S.M. Huang, H. Zheng, J. Ma, D.S. Sanchez, B. Wang, A. Bansil, F. Chou, P.P. Shibayev, H. Lin, S. Jia, M.Z. Hasan, Science 349(6248), 613 (2015). https://doi.org/10.1126/science.aaa9297. http://science.sciencemag.org/content/349/6248/613

  230. S.M. Huang, S.Y. Xu, I. Belopolski, C.C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, M.Z. Hasan, Nat. Commun. 6(1), 7373 (2015). https://doi.org/10.1038/ncomms8373

  231. X. Huang, L. Zhao, Y. Long, P. Wang, D. Chen, Z. Yang, H. Liang, M. Xue, H. Weng, Z. Fang, X. Dai, G. Chen, Phys. Rev. X 5, 031023 (2015). https://doi.org/10.1103/PhysRevX.5.031023

    Article  Google Scholar 

  232. B.Q. Lv, H.M. Weng, B.B. Fu, X.P. Wang, H. Miao, J. Ma, P. Richard, X.C. Huang, L.X. Zhao, G.F. Chen, Z. Fang, X. Dai, T. Qian, H. Ding, Phys. Rev. X 5, 031013 (2015). https://doi.org/10.1103/PhysRevX.5.031013

    Article  Google Scholar 

  233. H. Weng, C. Fang, Z. Fang, B.A. Bernevig, X. Dai, Phys. Rev. X 5, 011029 (2015). https://doi.org/10.1103/PhysRevX.5.011029

    Article  Google Scholar 

  234. B. Cheng, Y. Wang, D. Barbalas, T. Higo, S. Nakatsuji, N.P. Armitage, Appl. Phys. Lett. 115(1), 012405 (2019). https://doi.org/10.1063/1.5093414

    Article  ADS  Google Scholar 

  235. T. Matsuda, N. Kanda, T. Higo, N.P. Armitage, S. Nakatsuji, R. Matsunaga, Nat. Commun. 11(1), 909 (2020). https://doi.org/10.1038/s41467-020-14690-6

  236. Y. Gao, S. Kaushik, E.J. Philip, Z. Li, Y. Qin, Y.P. Liu, W.L. Zhang, Y.L. Su, X. Chen, H. Weng, D.E. Kharzeev, M.K. Liu, J. Qi, Nat. Commun. 11(1), 720 (2020). https://doi.org/10.1038/s41467-020-14463-1

  237. L. Prochaska, X. Li, D.C. MacFarland, A.M. Andrews, M. Bonta, E.F. Bianco, S. Yazdi, W. Schrenk, H. Detz, A. Limbeck, Q. Si, E. Ringe, G. Strasser, J. Kono, S. Paschen, Science 367(6475), 285 (2020). https://doi.org/10.1126/science.aag1595

    Article  ADS  Google Scholar 

  238. J. Mydosh, P. Oppeneer, Philos. Mag. 94(32–33), 3642 (2014). https://doi.org/10.1080/14786435.2014.916428

    Article  ADS  Google Scholar 

  239. H.B. Radousky, Magnetism in Heavy Fermion Systems (World Scientific, 2000). https://doi.org/10.1142/4460. https://www.worldscientific.com/doi/abs/10.1142/4460

  240. G. Bossé, L. Pan, Y.S. Li, L.H. Greene, J. Eckstein, N.P. Armitage, Phys. Rev. B 93, 085104 (2016). https://doi.org/10.1103/PhysRevB.93.085104

    Article  ADS  Google Scholar 

  241. M. Scheffler, T. Weig, M. Dressel, H. Shishido, Y. Mizukami, T. Terashima, T. Shibauchi, Y. Matsuda, J. Phys. Soc. Jpn. 82(4), 043712 (2013). https://doi.org/10.7566/JPSJ.82.043712

    Article  ADS  Google Scholar 

  242. J. Zhang, J. Yong, I. Takeuchi, R.L. Greene, R.D. Averitt, Phys. Rev. B 97, 155119 (2018). https://doi.org/10.1103/PhysRevB.97.155119

    Article  ADS  Google Scholar 

  243. Y. Cao, D. Chowdhury, D. Rodan-Legrain, O. Rubies-Bigorda, K. Watanabe, T. Taniguchi, T. Senthil, P. Jarillo-Herrero, Phys. Rev. Lett. 124, 076801 (2020). https://doi.org/10.1103/PhysRevLett.124.076801

    Article  ADS  Google Scholar 

  244. G. Seibold, R. Arpaia, Y.Y. Peng, R. Fumagalli, L. Braicovich, C. Di Castro, M. Grilli, G.C. Ghiringhelli, S. Caprara, Commun. Phys. 4(1), 7 (2021). https://doi.org/10.1038/s42005-020-00505-z

  245. B. Shen, Y. Zhang, Y. Komijani, M. Nicklas, R. Borth, A. Wang, Y. Chen, Z. Nie, R. Li, X. Lu, H. Lee, M. Smidman, F. Steglich, P. Coleman, H. Yuan, Nature 579(7797), 51 (2020). https://doi.org/10.1038/s41586-020-2052-z

    Article  ADS  Google Scholar 

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Acknowledgements

This work is supported by the ‘Department of Science and Technology’ under start-up research grant (Grant No. SRG/2019/000674). AB & SB thanks CSIR Govt. of India for Research Fellowship with Grant No. 09/080(1109)/2019-EMR-I & 09/080(1110)/2019-EMR-I, respectively. The concept for the paper was developed through discussions between all of the authors. The authors also acknowledge Dr. Kamaraju Natarajan, IISER Kolkata for the helpful discussion and comments.

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The original online version of this article was revised: In Figure 1, the temperature scale was wrong by 3 orders of magnitude (i.e. 1000). The scale label should have been “Temperature (mK)” instead of “Temperature (K)”. Figure 1 has been replaced accordingly.

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Bera, A., Bera, S., Kalimuddin, S. et al. Review of recent progress on THz spectroscopy of quantum materials: superconductors, magnetic and topological materials. Eur. Phys. J. Spec. Top. 230, 4113–4139 (2021). https://doi.org/10.1140/epjs/s11734-021-00216-8

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