Skip to main content
SpringerLink
Log in

Optical and Electrical Properties Topological Materials

  • Chapter
  • First Online:
Optical and Electrical Properties of Nanoscale Materials

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 318))

  • 1044 Accesses

Abstract

In this chapter, we present an overview of the structure, optical and electrical properties of materials that exhibit, or are predicted to exhibit, topological properties. We note that many of these materials consist of layers that are bonded by van der Waals forces and many have a local hexagonal structure. The materials are divided into those with a band gap and those without a band gap. We present the definitions of many of the key terms used in the topological description of materials as well as a description of the various types of topological materials such as topological insulators, Weyl semimetals, and Dirac semimetals. A useful and important part of this discussion is topological classification. For example, we describe the topological invariant \(\mathbb{Z}_{2}\). We present a brief overview of a tight binding, second quantization Hamiltonian that includes spin orbit and electron–electron interactions. Then we discuss materials with a band gap including the well-known tetradymites such as Bi2Se3 starting with a discussion of the crystal and electronic structure and resulting \(\mathbb{Z}_{2}\) classification. Next we present the optical and electrical properties of these materials. Whenever possible, experimental data for the dielectric functions are shown. Photoluminescence and Raman spectra are also shown, and the layer number dependence of the Raman spectra are discussed. This is followed by a similar discussion of gapped materials including Weyl semimetals, Dirac semimetals, and nodal line materials. When possible, experimental data is discussed in terms of whether or not topological properties are observed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. T.O. Wehling, A.M. Black-Schaffer, A.V. Balatsky, Dirac materials. Adv. Phys. 63, 1–76 (2014)

    Article  CAS  Google Scholar 

  2. T.-F. Chung, Y. Xu, Y.P. Chen, Transport measurements in twisted bilayer graphene: electron-phonon coupling and Landau level crossing. Phys. Rev. B 98, 035425 (2018)

    Google Scholar 

  3. Y. Ando, Topological insulator materials. J. Phys. Soc. Jpn. 82, 102001 (2013)

    Google Scholar 

  4. M.Z. Hasan, C.L. Kane, Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010)

    Article  CAS  Google Scholar 

  5. M.S. Dresselhaus, G. Dresselhaus, A. Jorio, Time reversal symmetry, in Group Theory (Springer, Berlin, 2008), pp. 403–430 (Chapter 16)

    Google Scholar 

  6. S.S. Chern, J. Simons, Characteristic forms and geometric invariants. Ann. Math. 99, 48–69 (1974)

    Article  Google Scholar 

  7. D.J. Thouless, M. Kohmoto, M.P. Nightingale, M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982)

    Article  CAS  Google Scholar 

  8. C.L. Kane, E.J. Mele, Z2 topological order and the quantum spin hall effect. Phys. Rev. Lett. 95, 146802 (2005)

    Google Scholar 

  9. L. Fu, C.L. Kane, Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007)

    Google Scholar 

  10. A. Bansil, H. Lin, T. Das, Colloquium: topological band theory. Rev. Mod. Phys. 88, 021004 (2016); C.L. Kane, Topological band theory and the Z2 invariant, in Topological Insulators, ed. by M. Franz, L. Molenkamp. Contemporary Concepts of Condensed Matter Science, vol. 6 (Elsevier, Amsterdam, 2013), pp. 1–324 (Chapter 1)

    Google Scholar 

  11. R.M. Kaufmann, D. Li, B. Wehefritz-Kaufmann, Notes on topological insulators. Rev. Math. Phys. 28, 1630003 (2016)

    Article  Google Scholar 

  12. H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, S.-C. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat. Phys. 5, 438–442 (2009)

    Article  CAS  Google Scholar 

  13. J.C.Y. Teo, L. Fu, C.L. Kane, Surface states and topological invariants in three-dimensional topological insulators: application to Bi1-xSbx. Phys. Rev. B 78, 045426 (2008)

    Google Scholar 

  14. Z. Song, S.-J. Huang, Y. Qi, C. Fang, M. Hermele, Topological states from topological crystals. Sci. Adv. 5, eaax2007 (2019)

    Google Scholar 

  15. M.G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B. Andrei Bernevig, Z. Wang, A complete catalogue of high-quality topological materials. Nature 566, 48–485 (2019)

    Google Scholar 

  16. A. Kitaev, Periodic Table for Topological Insulators and Superconductors (2009). arXiv:0901.2686v2 [cond-mat.mes-hall]

  17. B.-J. Yang, N. Nagaosa, Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nat. Comm. 5, 4898 (2014)

    Article  CAS  Google Scholar 

  18. F. Zhang, C.L. Kane, E.J. Mele, Topological mirror superconductivity. Phys. Rev. Lett. 111, 056403 (2013)

    Google Scholar 

  19. Y. Ueno, A. Yamakage, Y. Tanaka, M. Sato, Symmetry-protected majorana fermions in topological crystalline superconductors: theory and application to Sr2RuO4. Phys. Rev. Lett. 111, 087002 (2013)

    Google Scholar 

  20. B. Yan, C. Felser, Topological materials: Weyl semimetals. Ann. Rev. Cond. Mat. Phys. 8, 337–354 (2017)

    Article  Google Scholar 

  21. Z.K. Liu, L.X. Yang, Y. Sun, T. Zhang, H. Peng, H.F. Yang, C. Chen, Y. Zhang, Y.F. Guo, D. Prabhakaran, M. Schmidt, Z. Hussain, S.-K. Mo, C. Felser, B. Yan, Y.L. Chen, Evolution of the Fermi surface of Weyl semimetals in the transition metal pnictide family. Nat. Mat. 15, 27–31 (2016)

    Article  CAS  Google Scholar 

  22. A.A. Burkov, Topological semimetals. Nat. Mat. 15, 1145–1148 (2016)

    Article  CAS  Google Scholar 

  23. M.J. Klein, On a degeneracy theorem of Kramers. Am. J. Phys. 20(65), 65–71 (1952)

    Article  CAS  Google Scholar 

  24. G. Bian, T.-R. Chang, R. Sankar, S.-Y. Xu, H. Zheng, T. Neupert, C.-K. Chiu, S.-M. Huang, G. Chang, I. Belopolski, D.S. Sanchez, M. Neupane, N. Alidoust, C. Liu, B.K. Wang, C.-C. Lee, H.-T. Jeng, C. Zhang, Z. Yuan, S. Jia, A. Bansil, F. Chou, H. Lin, M.Z. Hasan, Topological nodal-line fermions in spin-orbit metal PbTaSe2. Nat. Comm. 7, 10556 (2016)

    Article  CAS  Google Scholar 

  25. H. Weng, X. Dai, Z. Fang, Transition-metal pentatellurides ZrTe5 and HfTe5: a paradigm for large-gap quantum spin hall insulators. Phys. Rev. X 4, 011002 (2014)

    Google Scholar 

  26. N. Varnava, D. Vanderbilt, Surfaces of axion insulators, Phys. Rev. B 98, 245117 (2018)

    Google Scholar 

  27. W. Witczak-Krempa, G. Chen, Y.B. Kim, L. Balents, Correlated quantum phenomena in the strong spin-orbit regime. Annu. Rev. Condens. Matter Phys. 5, 57–82 (2014)

    Article  CAS  Google Scholar 

  28. A.P. Mackenzie, Y. Maeno, Superconductivity of Sr2RuO4 and the physics of spin-triplet pairing. Rev. Mod. Phys. 75, 657–712 (2003)

    Article  CAS  Google Scholar 

  29. S. Koseki, N. Matsunaga, T. Asada, M.W. Schmidt, M.S. Gordon, Spin−orbit coupling constants in atoms and ions of transition elements: comparison of effective core potentials, model core potentials, and all-electron methods. J. Phys. Chem. A 123, 2325–2339 (2019)

    Article  CAS  Google Scholar 

  30. C. Mertens, M. Aichhorn, S. Biermann, Coulomb correlations in 4d and 5d oxides from first principles—or how spin–orbit materials choose their effective orbital degeneracies. Phys.: Condens. Matter. 29, 263001 (2017)

    Google Scholar 

  31. A.A. Burkov, M.D. Hook, L. Balents, Topological nodal semimetals. Phys. Rev. B 84, 235126 (2011)

    Google Scholar 

  32. M. Koshino, I.F. Hizbullah, Magnetic susceptibility in three-dimensional nodal semimetals. Phys. Rev. B 93, 045201 (2016)

    Google Scholar 

  33. R.Y. Chen, Z.G. Chen, X-Y Song, J.A. Schneeloch, G.D. Gu, F. Wang, N. Wang, Magneto-infrared spectroscopy of Landau levels and Zeeman splitting of three-dimensional massless Dirac Fermions in ZrTe5. Phys. Rev. Lett. 115, 176404 (2015)

    Google Scholar 

  34. N.P. Armitage, E.J. Mele, A. Vishwanath, Weyl and Dirac semimetals in three dimensional solids. Rev. Mod. Phys. 90, 015001 (2018)

    Google Scholar 

  35. D. Neubauer, J.P. Carbotte, A.A. Nateprov, A. Lohle, M. Dressel, A.V. Pronin, Interband optical conductivity of the [001]-oriented Dirac semimetal Cd3As2. Phys. Rev. B 93, 121202(R) (2016)

    Article  CAS  Google Scholar 

  36. K. Burch, Private communication

    Google Scholar 

  37. P. Hosur, S.A. Parameswaran, A. Vishwanath, Charge transport in Weyl semimetals. Phys. Rev. Lett. 108, 046602 (2012)

    Google Scholar 

  38. P.E.C. Ashby, J.P. Carbotte, Chiral anomaly and optical absorption in Weyl semimetals. Phys. Rev. B 89, 245121 (2014)

    Google Scholar 

  39. C.-Z. Chang, M. Li, Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators. J. Phys.: Condens. Matter 28, 123002 (2016)

    Google Scholar 

  40. S. Jia, S.-Y. Xu, M. Zahid Hasan, Weyl semimetals, Fermi arcs and chiral anomalies. Nat. Mat. 15, 1140–1144 (2016)

    Google Scholar 

  41. A. Akrap, M. Hakl, S. Tchoumakov, I. Crassee, J. Kuba, M.O. Goerbig, C.C. Homes, O. Caha, J. Novák, F. Teppe, W. Desrat, S. Koohpayeh, L. Wu, N.P. Armitage, A. Nateprov, E. Arushanov, Q. D. Gibson, R.J. Cava, D. van der Marel, B.A. Piot, C. Faugeras, G. Martinez, M. Potemski, M. Orlita, Magneto-optical signature of Massless Kane electrons in Cd3As2. Phys. Rev. Lett. 117, 136401 (2016)

    Google Scholar 

  42. Y. Jiang, J. Wang, T. Zhao, Z.L. Dun, Q. Huang, X.S. Wu, M. Mourigal, H.D. Zhou, W. Pan, M. Ozerov, D. Smirnov, Z. Jiang, Unraveling the topological phase of ZrTe5 via magneto-infrared spectroscopy. Phys. Rev. Lett. 125, 046403 (2020)

    Google Scholar 

  43. A.J. Green, S. Dey, Y.Q. An, B. O’Brien, S. J. O’Mullane, B. Thiel, A.C. Diebold, Surface oxidation of the topological insulator Bi2Se3. J. Vac. Sci. Technol. A 34, 061403 (2016)

    Google Scholar 

  44. S. Roy, H.L. Meyerheim, K. Mohseni, A. Ernst, M.M. Otrokov, M.G. Vergniory, G. Mussler, J. Kampmeier, D. Grützmacher, C. Tusche, J. Schneider, E.V. Chulkov, J. Kirschner, Atomic relaxations at the (0001) surface of Bi2Se3 single crystals and ultrathin films. Phys. Rev. B 90, 155456 (2014)

    Google Scholar 

  45. L.-L. Wang, M. Huang, S. Thimmaiah, A. Alam, S.L. Bud’ko, A. Kaminski, T.A. Lograsso, P. Canfield, D.D. Johnson, Native defects in tetradymite Bi2(TexSe3−x) topological insulators. Phys. Rev. B 87, 125303 (2013)

    Google Scholar 

  46. A.A. Reijnders, Y. Tian, L.J. Sandilands, G. Pohl, I.D. Kivlichan, S.Y. Frank Zhao, S. Jia, M.E. Charles, R.J. Cava, N. Alidoust, S. Xu, M. Neupane, M. Zahid Hasan, X. Wang, S.W. Cheong, K.S. Burch, Optical evidence of surface state suppression in Bi-based topological insulators. Phys. Rev. B 89, 075138 (2014)

    Google Scholar 

  47. Z. Ren, A.A. Taskin, S. Sasaki, K. Segawa, Y. Ando, Large bulk resistivity and surface quantum oscillations in the topological insulator Bi2Te2Se. Phys. Rev. B 82, 241306(R) (2010)

    Article  CAS  Google Scholar 

  48. E.K. de Vries, Thesis: Taking Topological Insulators for a Spin: Towards Understanding of Spin and Charge Transport in Bi2Se3 (Rijksuniversiteit Groningen, Groningen, 2017)

    Google Scholar 

  49. M. Bianchi, D. Guan, S. Bao, J. Mi, B. Brummerstedt Iversen, P.D.C. King, P. Hofmann, Coexistence of the topological state and a two-dimensional electron gas on the surface of Bi2Se3. Nat. Comm. 1, 128 (2010)

    Google Scholar 

  50. R.W.G. Wyckoff, Crystal Structures, vol. 2 (Wiley, New York, 1964)

    Google Scholar 

  51. J.P. Heremans, R.J. Cava, N. Samarth, Tetradymites as thermoelectrics and topological insulators. Nat. Rev. Mat. 2, 1–21 (2017)

    Google Scholar 

  52. D.S. Lee et al., Crystal structure, properties and nanostructuring of a new layered chalcogenide semiconductor, Bi2MnTe4. CrystEngComm 15, 5532–5538 (2013)

    Article  CAS  Google Scholar 

  53. M.M. Otrokov, I.P. Rusinov, M. Blanco-Rey, M. Hoffmann, A.Y. Vyazovskaya, S.V. Eremeev, A. Ernst, P.M. Echenique, A. Arnau, E.V. Chulkov, Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet MnBi2Te4 films. Phys. Rev. Lett. 122, 107202 (2019)

    Google Scholar 

  54. D. Zhang, M. Shi, T. Zhu, D. Xing, H. Zhang, J. Wang, Topological axion states in the magnetic insulator MnBi2Te4 with the quantized magnetoelectric effect. Phys. Rev. Lett. 122, 206401 (2019)

    Google Scholar 

  55. C. Liu, Y. Wang, H. Li, Y. Wu, Y. Li, J. Li, K. He, Y. Xu, J. Zhang, Y. Wang, Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator. Nat. Mat. 19, 522–527 (2020)

    Article  CAS  Google Scholar 

  56. W. Zhang, R. Yu, W. Feng, Y. Yao, H. Weng, X. Dai, Z. Fang, Topological aspect and quantum magnetoresistance of -Ag2Te. Phys. Rev. Lett. 106, 156808 (2011)

    Google Scholar 

  57. A. Sulaev, P. Ren, B. Xia, Q.H. Lin, T. Yu, C. Qiu, S.-Y. Zhang, M.-Y. Han, Z.P. Li, W.G. Zhu, Q. Wu, Y.P. Feng, L. Shen, S.-Q. Shen, L. Wang, Experimental evidences of topological surface states of β-Ag2Te. AIP Adv. 3, 032123 (2013)

    Google Scholar 

  58. S. Lee, J. In, Y. Yoo, Y. Jo, Y.C. Park, H.-J. Kim, H.C. Koo, J. Kim, B. Kim, K.L. Wang, Single crystalline β-Ag2Te nanowire as a new topological insulator. Nano Lett. 12, 4194−4199 (2012)

    Google Scholar 

  59. G. Manzoni, L. Gragnaniello, G. Autès, T. Kuhn, A. Sterzi, F. Cilento, M. Zacchigna, V. Enenkel, I. Vobornik, L. Barba, F. Bisti, Ph. Bugnon, A. Magrez, V. N. Strocov, H. Berger, O.V. Yazyev, M. Fonin, F. Parmigiani, A. Crepaldi, Evidence for a strong topological insulator phase in ZrTe5. Phys. Rev. Lett. 117, 237601 (2016)

    Google Scholar 

  60. P. Di Pietro, F. M. Vitucci, D. Nicoletti, L. Baldassarre, P. Calvani, R. Cava, Y. S. Hor, U. Schade, S. Lupi, Optical conductivity of bismuth-based topological insulators. Phys. Rev. B 86, 045439 (2012)

    Google Scholar 

  61. Y. Sharma, P. Srivastava, A. Dashora, L. Vadkhiya, M.K. Bhayani, R. Jain, A.R. Jani, B.L. Ahuja, Electronic structure, optical properties and Compton profiles of Bi2S3 and Bi2Se3. Solid State Sci. 14, 241 (2012)

    Article  CAS  Google Scholar 

  62. L.A. Walsh, A.J. Green, R. Addou, W. Nolting, C.R. Cormier, A.T. Barton, T.R. Mowll, R. Yue, N. Lu, N. Kim, M.J. Kim, V.P. LaBella, C. Ventrice, S. McDonnell, W.G. Vandenberghe, R.M. Wallace, A.C. Diebold, C.L. Hinkle, Fermi level manipulation through native doping in the topological insulator Bi2Se3. ACS Nano 12, 6310–6318 (2018)

    Article  CAS  Google Scholar 

  63. J. Humlíček, D. Hemzal, A. Dubroka, O. Caha, H. Steiner, G. Bauer, G. Springholz, Phys. Scr. T162, 14007 (2014)

    Article  CAS  Google Scholar 

  64. N.T. Mamedov, E.H. Alizade, Z.A. Jahangirli, Z.S. Aliev, N.A. Abdullayev, S.N. Mammadov, I.R. Amiraslanov, Y.-G. Shim, K. Wakita, S.S. Ragimov, A.I. Bayramov, M.B. Babanly, A.M. Shikin, E.V. Chulkov, Infrared spectroscopic ellipsometry and optical spectroscopy of plasmons in classic 3D topological insulators. J. Vac. Sci. Technol. B 37, 062602 (2020)

    Google Scholar 

  65. P.K. Das, T.J. Whitcher, M. Yang, X. Chi, Y.P. Feng, W. Lin, J.S. Chen, I. Vobornik, J. Fujii, K.A. Kokh, O.E. Tereshchenko, C.Z. Diao, J. Moon, S. Oh, A.H. Castro-Neto, M.B.H. Breese, A.T.S. Wee, A. Rusydi, Electronic correlation determining correlated plasmons in Sb-doped Bi2Se3. Phys. Rev. B 100, 115109 (2019)

    Google Scholar 

  66. K.M.F. Shahil, M.Z. Hossain, V. Goyal, A.A. Balandin, Micro-Raman spectroscopy of mechanically exfoliated few-quintuple layers of Bi2Te3, Bi2Se3 and Sb2Te3 materials. J. Appl. Phys. 111, 054305 (2012)

    Google Scholar 

  67. Z.A. Jahangirli, E.H. Alizade, Z.S. Aliev, M.M. Otrokov, N.A. Ismayilova, S.N. Mammadov, I.R. Amiraslanov, N.T. Mamedov, G.S. Orudjev, M.B. Babanly, A.M. Shikin, E.V. Chulkov, Electronic structure and dielectric function of Mn–Bi–Te layered compounds. J. Vac. Sci. Technol. B 37, 062910 (2019)

    Google Scholar 

  68. Z. Guo, H. Gu, M. Fang, B. Song, W. Wang, X. Chen, C. Zhang, H. Jiang, L. Wang, S. Liu, Complete dielectric tensor and giant optical anisotropy in quasi-one-dimensional ZrTe5. ACS Mater. Lett. 3, 525–534 (2021)

    Article  CAS  Google Scholar 

  69. A. Akrap, Private communication

    Google Scholar 

  70. R.Y. Chen, S.J. Zhang, J.A. Schneeloch, C. Zhang, Q. Li, G.D. Gu, N.L. Wang, Optical spectroscopy study of the three-dimensional Dirac semimetal ZrTe5. Phys. Rev. B 92, 075107 (2015)

    Google Scholar 

  71. E. Martino, I. Crassee, G. Eguchi, D. Santos-Cottin, R.D. Zhong, G.D. Gu, H. Berger, Z. Rukelj, M. Orlita, C.C. Homes, A. Akrap, Two-dimensional conical dispersion in ZrTe5 evidenced by optical spectroscopy. Phys. Rev. Lett. 122, 217402 (2019)

    Google Scholar 

  72. D. Santos-Cottin, M. Padlewski, E. Martino, S. Ben David, F. Le Mardelé, F. Capitani, F. Borondics, M. D. Bachmann, C. Putzke, P. J. W. Moll, R. D. Zhong, G. D. Gu, H. Berger, M. Orlita, C.C. Homes, Z. Rukelj, A. Akrap, Probing intraband excitations in ZrTe5: a high-pressure infrared and transport study. Phys. Rev. B 101, 125205 (2020)

    Google Scholar 

  73. Y.-X. Wang, F. Li, Examining the validity of the two-dimensional conical model to describe the three-dimensional ZrTe5. Phys. Rev. B 101, 195201 (2020)

    Article  CAS  Google Scholar 

  74. Z. Rukelj, C.C. Homes, M. Orlita, A. Akrap, Distinguishing the gapped and Weyl semimetal scenario in ZrTe5: insights from an effective two-band model. Phys. Rev. B 102, 125201 (2020)

    Article  CAS  Google Scholar 

  75. I. Crassee, E. Martino, C.C. Homes, O. Caha, J. Novák, P. Tückmantel, M. Hakl, A. Nateprov, E. Arushanov, Q.D. Gibson, R.J. Cava, S.M. Koohpayeh, K.E. Arpino, T.M. McQueen, M. Orlita, A. Akrap, Nonuniform carrier density in Cd3As2 evidenced by optical spectroscopy. Phys. Rev. B 97, 125204 (2018)

    Article  CAS  Google Scholar 

  76. G. Qiu, Y. Du, A. Charnas, H. Zhou, S. Jin, Z. Luo, D.Y. Zemlyanov, X. Xu, G.J. Cheng, P.D. Ye, Observation of optical and electrical in-plane anisotropy in high-mobility few-layer ZrTe5. Nano Lett. 16, 7364–7369 (2016)

    Article  CAS  Google Scholar 

  77. J. Wu, S. Zhang, L. Tong, J. Zhang, Raman spectroscopy of anisotropic two-dimensional materials, in Raman Spectroscopy of Two-Dimensional Materials, ed. by P.H. Tan (Springer Nature, Singapore, 2019), pp. 53–80 (Chapter 3)

    Google Scholar 

  78. J.G. Analytis, R.D. McDonald, S.C. Riggs, J.-H. Chu, G.S. Boebinger, I.R. Fisher, Two-dimensional surface state in the quantum limit of a topological insulator. Nat. Phys. 6, 960–964 (2010)

    Article  CAS  Google Scholar 

  79. Y. Deng, Y. Yu, M.Z. Shi, Z. Guo, Z. Xu, J. Wang, X.H. Chen, Y. Zhang, Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science 367, 895–900 (2020)

    Article  CAS  Google Scholar 

  80. S. Zhang, R. Wang, X. Wang, B. Wei, B. Chen, H. Wang, G. Shi, F. Wang, B. Jia, Y. Ouyang, F. Xie, F. Fei, M. Zhang, X. Wang, D. Wu, X. Wan, F. Song, H. Zhang, B. Wang, Experimental observation of the gate-controlled reversal of the anomalous hall effect in the intrinsic magnetic topological insulator MnBi2Te4 device. Nano Lett. 20, 709–714 (2019)

    Article  CAS  Google Scholar 

  81. T. Liang, J. Lin, Q. Gibson, S. Kushwaha, M. Liu, W. Wang, H. Xiong, J.A. Sobota, M. Hashimoto, P.S. Kirchmann, Z.-X. Shen, R.J. Cava, N.P. Ong, Anomalous Hall effect in ZrTe5. Nat. Phys. 14, 451–455 (2018)

    Article  CAS  Google Scholar 

  82. H. Xiong, J.A. Sobota, S.-L. Yang, H. Soifer, A. Gauthier, M.-H. Lu, Y.-Y. Lv, S.-H. Yao, D. Lu, M. Hashimoto, P.S. Kirchmann, Y.-F. Chen, Z.-X. Shen, Three-dimensional nature of the band structure of ZrTe5 measured by high-momentum-resolution photoemission spectroscopy. Phys. Rev. B 95, 195119 (2017)

    Article  Google Scholar 

  83. F. Tang, Y. Ren, P. Wang, R. Zhong, J. Schneeloch, S.A. Yang, K. Yang, P.A. Lee, G. Gu, Z. Qiao, L. Zhang, Three-dimensional quantum Hall effect and metal–insulator transition in ZrTe5. Nature 569, 537–542 (2019)

    Article  CAS  Google Scholar 

  84. X.-B. Li, W.-K. Huang, Y.-Y. Lv, K.-W. Zhang, C.-L. Yang, B.-B. Zhang, Y.B. Chen, S.-H. Yao, J. Zhou, M.-H. Lu, L. Sheng, S.-C. Li, J.-F. Jia, Q.-K. Xue, Y.-F. Chen, D.-Y. Xing, Experimental observation of topological edge states at the surface step edge of the topological insulator ZrTe5. Phys. Rev. Lett. 116, 176803 (2016)

    Article  CAS  Google Scholar 

  85. Q. Ma, S.-Y. Xu, C.-K. Chan, C.-L. Zhang, G. Chang, Y. Lin, W. Xie, T. Palacios, H. Lin, S. Jia, P.A. Lee, P. Jarillo-Herrero, N. Gedik, Direct optical detection of Weyl fermion chirality in a topological semimetal. Nat. Phys. 13, 842–847 (2017)

    Article  CAS  Google Scholar 

  86. A.A. Soluyanov, D. Gresch, Z. Wang, Q.-S. Wu, M. Troyer, X. Dai, B. Andrei Bernevig, Type-II Weyl semimetals. Nature 527, 495–498 (2015)

    Google Scholar 

  87. Y. Sun, S.-C. Wu, B. Yan, Topological surface states and Fermi arcs of the noncentrosymmetric Weyl semimetals TaAs, TaP, NbAs, and NbP. Phys. Rev. B 92, 115428 (2015)

    Google Scholar 

  88. D. Grassano, O. Pulci, A.M. Conte, F. Bechstedt, Validity of Weyl fermion picture for transition metals monopnictides TaAs, TaP, NbAs, and NbP from ab initio studies. Nat. Sci. Rep. 8, 3534 (2018)

    CAS  Google Scholar 

  89. S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B.K. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, M.Z. Hasan, A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Comm. 6, 7373 (2015)

    Article  CAS  Google Scholar 

  90. S. Furuseth, K. Selte, A. Kjekshus, On the arsenides and antimonides of Tantalum. Acta Chem. Scand. 19, 95 (1965)

    Article  CAS  Google Scholar 

  91. L. Ye, T. Suzuki, C.R. Wicker, J.G. Checkelsky, Extreme magnetoresistance in magnetic rare-earth monopnictides. Phys. Rev. B 97, 081108(R) (2018)

    Article  Google Scholar 

  92. C.-G. Duan, R.F. Sabirianov, W.N. Mei, P.A. Dowben, S.S. Jaswal, E.Y. Tsymbal, Electronic, magnetic and transport properties of rare-earth monopnictides. J. Phys.: Condens. Matter 19, 315220 (2007)

    Google Scholar 

  93. M. Zeng, C. Fang, G. Chang, Y.-A. Chen, T. Hsieh, A. Bansil, H. Lin, L. Fu, Topological semimetals and topological insulators in rare earth monopnictides. arXiv:1504.03492v1

  94. R. Lou, B.-B. Fu, Q.N. Xu, P.J. Guo, L.-Y. Kong, L.-K. Zeng, J.-Z. Ma, P. Richard, C. Fang, Y.-B. Huang, S.-S. Sun, Q. Wang, L. Wang, Y.-G. Shi, H.C. Lei, K. Liu, H.M. Weng, T. Qian, H. Ding, S.-C. Wang, Evidence of topological insulator state in the semimetal LaBi. Phys. Rev. B 95, 115140 (2017)

    Article  Google Scholar 

  95. J. Rossat-Mignod, P. Burlet, J. Villain, H. Bartholin, W. Tcheng-Si, D. Florence, O. Vogt, Phase diagram and magnetic structures of CeSb. Phys. Rev. B 16, 440–461 (1997)

    Article  Google Scholar 

  96. E. Tsymbal, Private communication

    Google Scholar 

  97. F.F. Tafti, Q.D. Gibson, S.K. Kushwaha, N. Haldolaarachchige, R.J. Cava, Resistivity plateau and extreme magnetoresistance in LaSb. Nat. Phys. 12, 272–277 (2016)

    Article  CAS  Google Scholar 

  98. S. Khalid, F.P. Sabino, A. Janotti, Topological phase transition in LaAs under pressure. Phys. Rev. B 98, 220102(R) (2018)

    Article  Google Scholar 

  99. N. Alidoust et al., A new form of (unexpected) Dirac fermions in the strongly-correlated cerium monopnictides. arXiv:1604.08571 [cond-mat.str-el] Table 1 in supplemental

  100. X. Wan, A.M. Turner, A. Vishwanath, S.Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011)

    Google Scholar 

  101. A.B. Sushkov, J.B. Hofmann, G.S. Jenkins, J. Ishikawa, S. Nakatsuji, S. Das Sarma, H.D. Drew, Optical evidence for a Weyl semimetal state in pyrochlore Eu2Ir2O7. Phys. Rev. B 92, 241108(R) (2015)

    Google Scholar 

  102. N. Taira, M. Wakeshima, Y. Hinatsu, Magnetic properties of iridium pyrochlores R2Ir2O7 R=Y, Sm, Eu and Lu. J. Phys.: Condens. Matter 13, 5527 (2001)

    Google Scholar 

  103. R.A. McCauley, Structural characteristics of pyrochlore formation. J. Appl. Phys. 51, 290–294 (1980)

    Article  CAS  Google Scholar 

  104. H. Zhang, K. Haule, D. Vanderbilt, Metal-insulator transition and topological properties of pyrochlore iridates. Phys. Rev. Lett. 118, 026404 (2017)

    Article  Google Scholar 

  105. G.L. Stamokostas, G.A. Fiete, Mixing of t2g-eg orbitals in 4d and 5d transition metal oxides. Phys. Rev. B 97, 085150 (2018)

    Article  CAS  Google Scholar 

  106. H. Kumar, K.C. Kharkwal, K. Kumar, K. Asokan, A. Banerjee, A.K. Pramanik, Magnetic and transport properties of the pyrochlore iridates (Y1−xPrx)Ir2O7: role of f-d exchange interaction and d-p orbital hybridization. Phys. Rev. B 101, 064405 (2020)

    Article  CAS  Google Scholar 

  107. J.P. Clancy, N. Chen, C.Y. Kim, W.F. Chen, K.W. Plumb, B.C. Jeon, T.W. Noh, Y.-J. Kim, Spin-orbit coupling in iridium-based 5d compounds probed by X-ray absorption spectroscopy. Phys. Rev. B 86, 195131 (2012)

    Article  CAS  Google Scholar 

  108. A.I. Liechtenstein, V.I. Anisimov, J. Zaane, Density functional theory: orbital ordering in Mott-Hubbard insulators. Phys. Rev. B 52, R5467 (1995)

    Article  CAS  Google Scholar 

  109. C. Berke, P. Michetti, C. Timm, Stability of the Weyl semimetal phase on the pyrochlore lattice. N. J. Phys. 20, 043057 (2018)

    Article  CAS  Google Scholar 

  110. V.K. Dwivedi, S. Mukhopadhyay, Influence of electronic structure parameters on the electrical transport and magnetic properties of Y2−xBixIr2O7 pyrochlore iridates. J. Appl. Phys. 126, 165–112 (2019)

    Article  CAS  Google Scholar 

  111. G. Chen, M. Hermele, Magnetic orders and topological phases from f-d exchange in pyrochlore iridates. Phys. Rev. B 86, 235129 (2012)

    Article  CAS  Google Scholar 

  112. J. Chakhalian, X. Liu, G.A. Fiete, Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures. APL Mater. 8, 050904 (2020)

    Article  CAS  Google Scholar 

  113. G.E. Topp, N. Tancogne-Dejean, A.F. Kemper, A. Rubio, M.A. Sentef, All-optical nonequilibrium pathway to stabilizing magnetic Weyl semimetals in pyrochlore iridates. Nat. Comm. 9, 4452 (2018)

    Article  CAS  Google Scholar 

  114. Y. Singh, P. Gegenwart, Antiferromagnetic Mott insulating state in single crystals of the honeycomb lattice material, Na2IrO3. Phys. Rev. B 82, 064–412 (2010)

    Article  Google Scholar 

  115. X. Liu, T. Berlijn, W.-G. Yin, W. Ku, A. Tsvelik, Y.-J. Kim, H. Gretarsson, Y. Singh, P. Gegenwart, J.P. Hill, Long-range magnetic ordering in Na2IrO3. Phys. Rev. B 83, 220403 (2011)

    Article  CAS  Google Scholar 

  116. C.H. Sohn, H.-S. Kim, T.F. Qi, D.W. Jeong, H.J. Park, H.K. Yoo, H.H. Kim, J.-Y. Kim, T.D. Kang, D.-Y. Cho, G. Cao, J. Yu, S.J. Moon, T.W. Noh, Mixing between Jeff =1/2 and 3/2 orbitals in Na2IrO3: a spectroscopic and density functional calculation study. Phys. Rev. B 88, 085125 (2013)

    Article  CAS  Google Scholar 

  117. S. Boseggia, R. Springell, H.C. Walker, A.T. Boothroyd, D. Prabhakaran, D. Wermeille, L. Bouchenoire, S.P. Collins, D.F. McMorrow, Antiferromagnetic order and domains in Sr3Ir2O7 probed by X-ray resonant scattering. Phys. Rev. B 85, 184432 (2012)

    Article  CAS  Google Scholar 

  118. B.J. Kim, H. Jin, S.J. Moon, J.-Y. Kim, B.-G. Park, C.S. Leem, J. Yu, T.W. Noh, C. Kim, S.-J. Oh, J.-H. Park, V. Durairaj, G. Cao, E. Rotenberg, Novel Jeff = 1/2 Mott State induced by relativistic spin-orbit coupling in Sr2IrO4. Phys. Rev. Lett. 101, 076402 (2008)

    Article  CAS  Google Scholar 

  119. F. Ye, S. Chi, B.C. Chakoumakos, J.A. Fernandez-Baca, T. Qi, G. Cao, Magnetic and crystal structures of Sr2IrO4: a neutron diffraction study. Phys. Rev. B 87, 140406(R) (2013)

    Article  CAS  Google Scholar 

  120. S. Fujiyama, K. Ohashi, H. Ohsumi, K. Sugimoto, T. Takayama, T. Komesu, M. Takata, T. Arima, H. Takagi, Weak antiferromagnetism of Jeff = 12 band in bilayer iridate Sr3Ir2O7. Phys. Rev. B 86, 174414 (2012)

    Article  CAS  Google Scholar 

  121. P.D.C. King, T. Takayama, A. Tamai, E. Rozbicki, S. McKeown Walker, M. Shi, L. Patthey, R.G. Moore, D. Lu, K.M. Shen, H. Takagi, F. Baumberger, Spectroscopic indications of polaronic behavior of the strong spin-orbit insulator Sr3Ir2O7. Phys. Rev. B 87, 241106(R) (2013)

    Article  CAS  Google Scholar 

  122. Z. Zhao, S. Wang, T.F. Qi, Q. Zeng, S. Hirai, P.P. Kong, L. Li, C. Park, S.J. Yuan, C.Q. Jin, G. Cao, W.L. Mao, Pressure induced second-order structural transition in Sr3Ir2O7. J. Phys. Condens. Matter 26, 215402 (2014)

    Article  CAS  Google Scholar 

  123. M.K. Crawford, M.A. Subramanian, R.L. Harlow, J.A. Fernandez-Baca, Z.R. Wang, D.C. Johnston, Structural and magnetic studies of Sr2IrO4. Phys. Rev. B 49, 9198–9201 (1994)

    Article  CAS  Google Scholar 

  124. W. Al-Sawai, H. Lin, R.S. Markiewicz, L.A. Wray, Y. Xia, S.-Y. Xu, M.Z. Hasan, A. Bansil, Topological electronic structure in half-Heusler topological insulators. Phys. Rev. B 82, 125208 (2010)

    Article  CAS  Google Scholar 

  125. H. Lin, L.A. Wray, Y. Xia, S. Xu, S. Jia, R.J. Cava, A. Bansil, M. Zahid Hasan, Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena. Nat. Mater 9, 546–549 (2010)

    Article  CAS  Google Scholar 

  126. S. Chadov, X. Qi, J. Kübler, G.H. Fecher, C. Felser, S.C. Zhang, Tunable multifunctional topological insulators in ternary Heusler compounds. Nat. Mat. 9, 541–545 (2010)

    Article  CAS  Google Scholar 

  127. H.C. Kandpal, C. Felser, R. Seshadri, Covalent bonding and the nature of band gaps in some half-Heusler compounds. J. Phys. D: Appl. Phys. 39, 776–785 (2006). https://doi.org/10.1088/0022-3727/39/5/S02

    Article  CAS  Google Scholar 

  128. C. Shekhar, N. Kumar, V. Grinenko, S. Singh, R. Sarkar, H. Luetkens, S.-C. Wu, Y. Zhang, A.C. Komarek, E. Kampert, Y. Skourski, J. Wosnitza, W. Schnelle, A. McCollam, U. Zeitler, J. Kübler, B. Yan, H.-H. Klauss, S.S.P. Parkin, C. Felser, Anomalous hall effect in Weyl semimetal half-Heusler compounds RPtBi (R=Gd and Nd). NAS 115, 9140–9144 (2018)

    Article  CAS  Google Scholar 

  129. D. Di Sante, P.K. Das, C. Bigi, Z. Ergönenc, N. Gürtler, J.A. Krieger, T. Schmitt, M.N. Ali, G. Rossi, R. Thomale, C. Franchini, S. Picozzi, J. Fujii, V.N. Strocov, G. Sangiovanni, I. Vobornik, R.J. Cava, G. Panaccione, Three-dimensional electronic structure of the type-II Weyl semimetal WTe2. Phys. Rev. Lett. 119, 026403 (2017)

    Article  Google Scholar 

  130. A.J. Frenzel, C.C. Homes, Q.D. Gibson, Y.M. Shao, K.W. Post, A. Charnukha, R.J. Cava, D.N. Basov, Anisotropic electrodynamics of type-II Weyl semimetal candidate WTe2. Phys. Rev. B 95, 245140 (2017)

    Article  Google Scholar 

  131. M.N. Ali, J. Xiong, S. Flynn, J. Tao, Q.D. Gibson, L.M. Schoop, T. Liang, N. Haldolaarachchige, M. Hirschberger, N.P. Ong, R.J. Cava, Large, non-saturating magnetoresistance in WTe2. Nature 514, 205–208 (2014)

    Article  CAS  Google Scholar 

  132. L.S. Xie, L.M. Schoop, E.M. Seibel, Q.D. Gibson, W. Xie, R.J. Cava, A new form of Ca3P2 with a ring of Dirac nodes. APL Mat. 3, 083602 (2015). https://doi.org/10.1063/1.4926545

    Article  CAS  Google Scholar 

  133. Y.-H. Chan, C.-K. Chiu, M.Y. Chou, A.P. Schnyder, Ca3P2 and other topological semimetals with line nodes and drumhead surface states. Phys. Rev. B 93, 205132 (2016)

    Article  CAS  Google Scholar 

  134. Z. Wang, H. Weng, Q. Wu, X. Dai, Z. Fang, Three-dimensional Dirac semimetal and quantum transport in Cd3As2. Phys. Rev. B 88, 125427 (2013)

    Article  CAS  Google Scholar 

  135. M.N. Ali, Q. Gibson, S. Jeon, B.B. Zhou, A. Yazdani, R.J. Cava, The crystal and electronic structures of Cd3As2, the three-dimensional electronic analogue of graphene. Inorg. Chem. 53, 4062–4067 (2014)

    Article  CAS  Google Scholar 

  136. I. Crassee, R. Sankar, W.-L. Lee, A. Akrap, M. Orlita, 3D Dirac semimetal Cd3As2: a review of material properties. Phys. Rev. Matter. 2, 120302 (2018)

    CAS  Google Scholar 

  137. E.O. Kane, Band structure of indium antimonide. J. Phys. Chem. Solids 1, 249–261 (1957)

    Article  Google Scholar 

  138. S.L. Chuang, C.S. Chang, k.p method for strained wurtzite semiconductors. Phys. Rev. B 54, 2491–2504 (1996)

    Article  CAS  Google Scholar 

  139. J. Bodnar, Band structure of Cd3As2 from Shubnikov—de Haas and de Haas—van Alphen effects, in Proceedings of the III International Conference, Warsaw, 1977, ed. by J. Raułuszkiewicz, M. Górska, E. Kaczmarek (Elsevier, New York, 1977), p. 311

    Google Scholar 

  140. L.C. Lew Yan Voon, M. Willatzen, The k·p Method: Electronic Properties of Semiconductors (Springer, Berlin, 2009). See p. 19 for the definition of parameters L, M, and P and 55–64 for a discussion of the four-band Kane model

    Google Scholar 

  141. T. Schumann, L. Galletti, D.A. Kealhofer, H. Kim, M. Goyal, S. Stemmer, Observation of the quantum hall effect in confined films of the three-dimensional Dirac semimetal Cd3As2. Phys. Rev. Lett. 120, 016801 (2018)

    Article  CAS  Google Scholar 

  142. Z. Wang, Y. Sun, X.-Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, Z. Fang, Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb). Phys. Rev. B 85, 195320 (2012)

    Article  CAS  Google Scholar 

  143. S.K. Kushwaha, J.W. Krizan, B.E. Feldman, A. Gyenis, M.T. Randeria, J. Xiong, S.-Y. Xu, N. Alidoust, I. Belopolski, Bulk crystal growth and electronic characterization of the 3D Dirac semimetal Na3Bi. APL Mat. 3, 041504 (2015)

    Article  CAS  Google Scholar 

  144. K.-H. Ahn, K.-W. Lee, W.E. Pickett, Spin-orbit interaction driven collective electron-hole excitations in a noncentrosymmetric nodal loop Weyl semimetal. Phys Rev. B 92, 115149 (2015)

    Article  CAS  Google Scholar 

  145. 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, X.G. Qiu, Optical spectroscopy of the Weyl semimetal TaAs. Phys. Rev. B 93, 121110(R) (2016)

    Article  CAS  Google Scholar 

  146. D. Neubauer, A. Yaresko, W. Li, A. Löhle, R. Hübner, M.B. Schilling, C. Shekhar, C. Felser, M. Dressel, A.V. Pronin, Optical conductivity of the Weyl semimetal NbP. Phys. Rev. B 98, 195203 (2018)

    Article  CAS  Google Scholar 

  147. S. Polatkan, M.O. Goerbig, J. Wyzula, R. Kemmler, L.Z. Maulana, B.A. Piot, I. Crassee, A. Akrap, C. Shekhar, C. Felser, M. Dressel, A.V. Pronin, M. Orlita, Magneto-optics of a Weyl semimetal beyond the conical band approximation: case study of TaP. Phys. Rev. Lett. 124, 176402 (2020)

    Article  CAS  Google Scholar 

  148. Y.S. Kwon, M. Takeshigea, O. Nakamurab, T. Suzuki, T. Kasuya, On the common feature of the optical reflectivity in rare-earth monopnictides due to 5d electron screening. Phys. B 171, 316–319 (1991)

    Article  CAS  Google Scholar 

  149. K. Ueda, J. Fujioka, Y. Tokura, Variation of optical conductivity spectra in the course of bandwidth-controlled metal-insulator transitions in pyrochlore iridates. Phys. Rev. B 93, 245120 (2016)

    Article  Google Scholar 

  150. K. Matasuhira, M. Wakashima, R. Nakakanishi, T. Yamada, A. Nakamura, W. Kawano, S. Takagi, Y. Hinatsu, Metal-insulator transition in pyrochlore iridates Ln2Ir2O7 (Ln=Nd, Sm, and Eu). J. Phys. Soc. Jpn. 76, 043706 (2001)

    Article  CAS  Google Scholar 

  151. J.P. Carbotte, Optical response of line node semimetal. J. Phys. Condens. Matter 29, 045301 (2017)

    Article  CAS  Google Scholar 

  152. R.W. Godby, P. García-González, Density functional theories and self-energy approaches, in A Primer in Density Functional Theory, vol. 620, ed. by C. Fiolhais, F. Nogueira, M.A.L. Marques. Lecture Notes in Physics (Springer, Berlin, 2003), pp. 185–217

    Google Scholar 

  153. A.A. Burkov, Anomalous hall effect in Weyl metals. Phys. Rev. Lett. 113, 187202 (2014)

    Article  CAS  Google Scholar 

  154. Y. Sun, Y. Zhang, C. Felser, B. Yan, Strong intrinsic spin hall effect in the TaAs family of Weyl semimetals. Phys. Rev. Lett. 117, 146403 (2016)

    Article  CAS  Google Scholar 

  155. X. Huang, L. Zhao, Y. Long, P. Wang, D. Chen, Z. Yang, H. Liang, M. Xue, H. Weng, Z. Fang, X. Dai, G. Chen, Observation of the chiral-anomaly-induced negative magnetoresistance in 3D weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015)

    Google Scholar 

  156. N.J. Ghimire, Y. Luo, M. Neupane, D.J. Williams, E.D. Bauer, F. Ronning, Magnetotransport of single crystalline NbAs. J. Phys. Condens. Matter 27, 152201 (2015)

    Article  CAS  Google Scholar 

  157. K.-Y. Yang, Y.-M. Lu, Y. Ran, Quantum Hall effects in a Weyl semimetal: possible application in pyrochlore iridates. Phys. Rev. B 84, 075129 (2011)

    Article  CAS  Google Scholar 

  158. S.M. Disseler, S.R. Giblin, C. Dhital, K.C. Lukas, S.D. Wilson, M.J. Graf, Magnetization and Hall effect studies on the pyrochlore iridate Nd2Ir2O7. Phys. Rev. B 87, 060403(R) (2013)

    Article  CAS  Google Scholar 

  159. Y. Machida, S. Nakatsuji, S. Onoda, T. Tayama, T. Sakakibara, Time-reversal symmetry breaking and spontaneous Hall effect without magnetic dipole order. Nature 463, 210–213 (2010)

    Article  CAS  Google Scholar 

  160. S. Tang, C. Zhang, D. Wong, Z. Pedramrazi, H.-Z. Tsai, C. Jia, B. Moritz, M. Claassen, H. Ryu, S. Kahn, J. Jiang, H. Yan, M. Hashimoto, D. Lu, R.G. Moore, C.-C. Hwang, C. Hwang, Z. Hussain, Y. Chen, M.M. Ugeda, Z. Liu, X. Xie, T.P. Devereaux, M.F. Crommie, S.-K. Mo, Z.-X. Shen, Quantum spin Hall state in monolayer 1 T′-WTe2. Nat. Phys. 13, 683–688 (2017)

    Article  CAS  Google Scholar 

  161. T.-R. Chang, P.-J. Chen, G. Bian, S.-M. Huang, H. Zheng, T. Neupert, R. Sankar, S.-Y. Xu, I. Belopolski, G. Chang, B.-K. Wang, F. Chou, A. Bansil, H.-T. Jeng, H. Lin, M. Zahid Hasan, Topological Dirac surface states and superconducting pairing correlations in PbTaSe2. Phys. Rev. B 93, 245130 (2016)

    Article  Google Scholar 

  162. S.-Y. Guan, P.-J. Chen, M.-W. Chu, R. Sankar, F. Chou, H.-T. Jeng, C.-S. Chang, T.-M. Chuang, Superconducting topological surface states in the noncentrosymmetric bulk superconductor PbTaSe2. Sci. Adv. 2, e1600894 (2016)

    Article  CAS  Google Scholar 

  163. T. Schumann, M. Goyal, D.A. Kealhofer, S. Stemmer, Negative magnetoresistance due to conductivity fluctuations in films of the topological semimetal Cd3As2. Phys. Rev. B 95, 241113(R) (2017)

    Article  Google Scholar 

  164. J. Xiong, S. Kushwaha, J. Krizan, T. Liang, R.J. Cava, N.P. Ong, Anomalous conductivity tensor in the Dirac semimetal Na3Bi. EPL 114, 27002 (2016)

    Article  CAS  Google Scholar 

  165. J. Xiong, S.K. Kushwaha, T. Liang, J.W. Krizan, M. Hirschberger, W. Wang, R.J. Cava, N.P. Ong, Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413–416 (2015)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SUNY Polytechnic Institute, Albany, NY, USA

    Alain Diebold

  2. Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC, USA

    Tino Hofmann

Authors
  1. Alain Diebold
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tino Hofmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alain Diebold .

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Diebold, A., Hofmann, T. (2021). Optical and Electrical Properties Topological Materials. In: Optical and Electrical Properties of Nanoscale Materials. Springer Series in Materials Science, vol 318. Springer, Cham. https://doi.org/10.1007/978-3-030-80323-0_9

Download citation

Publish with us

Policies and ethics

Search

Navigation