World Scientific
  • Search
    Quick Search in Journals
    Access type:
    Quick Search anywhere
    Access type:
    Advanced Search
  • My Cart
  •   
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×

Our site uses Javascript to enchance its usability.You can disable your ad blocker or whitelist our website www.worldscientific.com to view the full content.

Select your blocker:

Adblock Plus Instructions

  1. Click the AdBlock Plus icon in the extension bar
  2. Click the blue power button
  3. Click refresh

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at [email protected] for any enquiries.
Special Issue on Advanced Spintronics in Novel Materials and its Applications; Guest Editor: Mansoor Bin Abdul Jalil (National University of Singapore)No Access

Dirac and Weyl Materials: Fundamental Aspects and Some Spintronics Applications

    https://doi.org/10.1142/S2010324716400038Cited by:112 (Source: Crossref)
    Previous
    Next

    Abstract

    Dirac and Weyl materials refer to a class of solid materials which host low-energy quasiparticle excitations that can be described by the Dirac and Weyl equations in relativistic quantum mechanics. Starting with the advent of graphene as the first prominent example, these materials have been attracting tremendous interest owing to their novel fundamental properties as well as the great potential for applications. Here we introduce the basic concepts and notions related to Dirac and Weyl materials and briefly review some recent works in this field, particularly on the conceptual development and the possible spintronics/pseudospintronics applications.

    References

    • 1. P. A. M. Dirac, Proc. R. Soc. London A Mathematical, Physical and Engineering Sciences 117, 610 (1928). Crossref, Google Scholar
    • 2. G. E. Volovik, The Universe in a Helium Droplet (Oxford University Press, 2009). Crossref, Google Scholar
    • 3. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, Science 306, 666 (2004). Crossref, Google Scholar
    • 4. M. Xu, T. Liang, M. Shi and H. Chen, Chem. Rev. 113, 3766 (2013). Crossref, Google Scholar
    • 5. S. Z. Butler, S. M. Hollen, L. Cao, Y. Cui, J. A. Gupta, H. R. Gutirrez, 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 and J. E. Goldberger, ACS Nano 7, 2898 (2013). Crossref, Google Scholar
    • 6. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). Crossref, Google Scholar
    • 7. H. Nielsen and M. Ninomiya, Nucl. Phys. B 185, 20 (1981). Crossref, Google Scholar
    • 8. H. Nielsen and M. Ninomiya, Nucl. Phys. B 193, 173 (1981). Crossref, Google Scholar
    • 9. D. Pesin and A. H. MacDonald, Nat. Mater. 11, (2012) 409. Crossref, Google Scholar
    • 10. O. Vafek and A. Vishwanath, Ann. Rev. Condens. Matter Physics 5 (2014). Crossref, Google Scholar
    • 11. T. Wehling, A. Black-Schaffer and A. Balatsky, Adv. Phys. 63, 1 (2014). Crossref, Google Scholar
    • 12. Q. D. Gibson, L. M. Schoop, L. Muechler, L. S. Xie, M. Hirschberger, N. P. Ong, R. Car and R. J. Cava, Phys. Rev. B 91, 205128 (2015). Crossref, Google Scholar
    • 13. B. Yan and C. Felser, Annu. Rev. Condens. Matter Phys. (2016). Google Scholar
    • 14. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Cengage Learning, 1976). Google Scholar
    • 15. D. Xiao, M.-C. Chang and Q. Niu, Rev. Mod. Phys. 82, 1959 (2010). Crossref, Google Scholar
    • 16. M. V. Berry, Proc. R. Soc. London A, Math. Phys. Engineering Sciences 392 (1984) 45. Crossref, Google Scholar
    • 17. A. P. Schnyder, S. Ryu, A. Furusaki and A. W. W. Ludwig, Phys. Rev. B 78 (2008) 195125. Crossref, Google Scholar
    • 18. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005). Crossref, Google Scholar
    • 19. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005). Crossref, Google Scholar
    • 20. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman and M. S. Strano, Nat. Nano 7, 699 (2012). Crossref, Google Scholar
    • 21. D. Xiao, G.-B. Liu, W. Feng, X. Xu and W. Yao, Phys. Rev. Lett. 108, 196802 (2012). Crossref, Google Scholar
    • 22. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010). Crossref, Google Scholar
    • 23. X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011). Crossref, Google Scholar
    • 24. Y. Yao, F. Ye, X.-L. Qi, S.-C. Zhang and Z. Fang, Phys. Rev. B 75, 041401 (2007). Crossref, Google Scholar
    • 25. H. Min, J. E. Hill, N. A. Sinitsyn, B. R. Sahu, L. Kleinman and A. H. MacDonald, Phys. Rev. B 74, 165310 (2006). Crossref, Google Scholar
    • 26. C.-C. Liu, W. Feng and Y. Yao, Phys. Rev. Lett. 107, 076802 (2011). Crossref, Google Scholar
    • 27. Y. Xu, B. Yan, H.-J. Zhang, J. Wang, G. Xu, P. Tang, W. Duan and S.-C. Zhang, Phys. Rev. Lett. 111, 136804 (2013). Crossref, Google Scholar
    • 28. Y. H. Lu, D. Zhou, T. Wang, S. A. Yang and J. Z. Jiang, Sci. Rep. 6, 21723 (2016). Crossref, Google Scholar
    • 29. C.-C. Liu, H. Jiang and Y. Yao, Phys. Rev. B 84, 195430 (2011). Crossref, Google Scholar
    • 30. M. Ezawa, Phys. Rev. Lett. 109, 055502 (2012). Crossref, Google Scholar
    • 31. W.-F. Tsai, C.-Y. Huang, T.-R. Chang, H. Lin, H.-T. Jeng and A. Bansil, Nat. Commun. 4, 1500 (2013). Crossref, Google Scholar
    • 32. S. A. Yang, H. Pan and F. Zhang, RSC Adv. 5, 83350 (2015). Crossref, Google Scholar
    • 33. Z. Song, C.-C. Liu, J. Yang, J. Han, M. Ye, B. Fu, Y. Yang, Q. Niu, J. Lu and Y. Yao, NPG Asia Mater. 6 (2014) e147. Crossref, Google Scholar
    • 34. C.-C. Liu, S. Guan, Z. Song, S. A. Yang, J. Yang and Y. Yao, Phys. Rev. B 90, 085431 (2014). Crossref, Google Scholar
    • 35. S.-Q. Shen, Topological Insulators: Dirac Equation in Condensed Matters (Springer, 2013). Google Scholar
    • 36. J. Wang, S. Deng, Z. Liu and Z. Liu, Natl. Sci. Rev. 2, 22 (2015). Crossref, Google Scholar
    • 37. D. Malko, C. Neiss, F. Viñes and A. Görling, Phys. Rev. Lett. 108, 086804 (2012). Crossref, Google Scholar
    • 38. L.-C. Xu, R.-Z. Wang, M.-S. Miao, X.-L. Wei, Y.-P. Chen, H. Yan, W.-M. Lau, L.-M. Liu and Y.-M. Ma, Nanoscale 6, 1113 (2014). Crossref, Google Scholar
    • 39. X.-F. Zhou, X. Dong, A. R. Oganov, Q. Zhu, Y. Tian and H.-T. Wang, Phys. Rev. Lett. 112, 085502 (2014). Crossref, Google Scholar
    • 40. G. Liu, S. B. Liu, B. Xu, C. Y. Ouyang, H. Y. Song, S. Guan and S. A. Yang, J. Phys. Chem. Lett. 6, 4936 (2015). Crossref, Google Scholar
    • 41. Y. Lu, D. Zhou, G. Chang, S. Guan, W. Chen, Y. Jiang, J. Jiang, X.-S. Wang, S. A. Yang, Y. P. Feng, Y. Kawazoe and H. Lin, Npj Comput. Mater. 2, 16011 (2016). Crossref, Google Scholar
    • 42. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen and Y. Zhang, Nat. Nano 9, 372 (2014). Crossref, Google Scholar
    • 43. Y. Lu, W. Xu, M. Zeng, G. Yao, L. Shen, M. Yang, Z. Luo, F. Pan, K. Wu, T. Das, P. He, J. Jiang, J. Martin, Y. P. Feng, H. Lin and X.-S. Wang, Nano Lett. 15, 80 (2014). Crossref, Google Scholar
    • 44. S. M. Young and C. L. Kane, Phys. Rev. Lett. 115, 126803 (2015). Crossref, Google Scholar
    • 45. Z. Wang, A. Alexandradinata, R. J. Cava and B. A. Bernevig, Nature 532, 189 (2016). Crossref, Google Scholar
    • 46. S. Murakami, New J. Phys. 9, 356 (2007). Crossref, Google Scholar
    • 47. X. Wan, A. M. Turner, A. Vishwanath and S. Y. Savrasov, Phys. Rev. B 83, 205101 (2011). Crossref, Google Scholar
    • 48. A. A. Burkov and L. Balents, Phys. Rev. Lett. 107, 127205 (2011). Crossref, Google Scholar
    • 49. L. Lu, L. Fu, J. D. Joannopoulos and M. Soljacic, Nat. Photon. 7, 294 (2013). Crossref, Google Scholar
    • 50. M. Gong, S. Tewari and C. Zhang, Phys. Rev. Lett. 107, 195303 (2011). Crossref, Google Scholar
    • 51. H. Weng, C. Fang, Z. Fang, B. A. Bernevig and X. Dai, Phys. Rev. X 5, 011029 (2015). Google Scholar
    • 52. 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 and M. Z. Hasan, Nat. Commun. 6, 7373 (2015). Crossref, Google Scholar
    • 53. 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 and M. Z. Hasan, Science 349, 613 (2015). Crossref, Google Scholar
    • 54. 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 and H. Ding, Phys. Rev. X 5, 031013 (2015). Google Scholar
    • 55. L. X. Yang, Z. K. Liu, Y. Sun, H. Peng, H. F. Yang, T. Zhang, B. Zhou, Y. Zhang, Y. F. Guo, M. Rahn, D. Prabhakaran, Z. Hussain, S.-K. Mo, C. Felser, B. Yan and Y. L. Chen, Nat. Phys. 11, 728 (2015). Crossref, Google Scholar
    • 56. B. Q. Lv, N. Xu, H. M. Weng, J. Z. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, C. E. Matt, F. Bisti, V. N. Strocov, J. Mesot, Z. Fang, X. Dai, T. Qian, M. Shi and H. Ding, Nat Phys 11, 724 (2015). Crossref, Google Scholar
    • 57. S. M. Young, S. Zaheer, J. C. Y. Teo, C. L. Kane, E. J. Mele and A. M. Rappe, Phys. Rev. Lett. 108, 140405 (2012). Crossref, Google Scholar
    • 58. Z. Wang, Y. Sun, X.-Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai and Z. Fang, Phys. Rev. B 85, 195320 (2012). Crossref, Google Scholar
    • 59. Z. Wang, H. Weng, Q. Wu, X. Dai and Z. Fang, Phys. Rev. B 88, 125427 (2013). Crossref, Google Scholar
    • 60. X. Xiao, S. A. Yang, Z. Liu, H. Li and G. Zhou, Sci. Rep. 5, 7898 (2015). Crossref, Google Scholar
    • 61. B. A. Bernevig, T. L. Hughes and S.-C. Zhang, Science 314, 1757 (2006). Crossref, Google Scholar
    • 62. S.-Y. Xu, C. Liu, S. K. Kushwaha, R. Sankar, J. W. Krizan, I. Belopolski, M. Neupane, G. Bian, N. Alidoust, T.-R. Chang, H.-T. Jeng, C.-Y. Huang, W.-F. Tsai, H. Lin, P. P. Shibayev, F.-C. Chou, R. J. Cava and M. Z. Hasan, Science 347, 294 (2015). Crossref, Google Scholar
    • 63. G. Xu, H. Weng, Z. Wang, X. Dai and Z. Fang, Phys. Rev. Lett. 107, 186806 (2011). Crossref, Google Scholar
    • 64. C. Fang, M. J. Gilbert, X. Dai and B. A. Bernevig, Phys. Rev. Lett. 108, 266802 (2012). Crossref, Google Scholar
    • 65. A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai and B. A. Bernevig, Nature 527, 495 (2015). Crossref, Google Scholar
    • 66. Y. Xu, F. Zhang and C. Zhang, Phys. Rev. Lett. 115, 265304 (2015). Crossref, Google Scholar
    • 67. Y. Chen, Y. Xie, S. A. Yang, H. Pan, F. Zhang, M. L. Cohen and S. Zhang, Nano Lett. 15, 6974 (2015). Crossref, Google Scholar
    • 68. M. Phillips and V. Aji, Phys. Rev. B 90, 115111 (2014). Crossref, Google Scholar
    • 69. H. Weng, Y. Liang, Q. Xu, R. Yu, Z. Fang, X. Dai and Y. Kawazoe, Phys. Rev. B 92, 045108 (2015). Crossref, Google Scholar
    • 70. K. Mullen, B. Uchoa and D. T. Glatzhofer, Phys. Rev. Lett. 115, 026403 (2015). Crossref, Google Scholar
    • 71. R. Yu, H. Weng, Z. Fang, X. Dai and X. Hu, Phys. Rev. Lett. 115, 036807 (2015). Crossref, Google Scholar
    • 72. Y. Kim, B. J. Wieder, C. L. Kane and A. M. Rappe, Phys. Rev. Lett. 115, 036806 (2015). Crossref, Google Scholar
    • 73. Y. Chen, Y.-M. Lu and H.-Y. Kee, Nat. Commun. 6 (2015). Google Scholar
    • 74. Q.-F. Liang, J. Zhou, R. Yu, Z. Wang and H. Weng, Phys. Rev. B 93, 085427 (2016). Crossref, Google Scholar
    • 75. Y. X. Zhao and Z. D. Wang, Phys. Rev. Lett. 110, 240404 (2013). Crossref, Google Scholar
    • 76. C. Fang, Y. Chen, H.-Y. Kee and L. Fu, Phys. Rev. B 92, 081201 (2015). Crossref, Google Scholar
    • 77. C. Zhong, Y. Chen, Y. Xie, S. A. Yang, M. L. Cohen and S. B. Zhang, Nanoscale 8, 7232 (2016). Crossref, Google Scholar
    • 78. S. A. Yang, H. Pan and F. Zhang, Phys. Rev. Lett. 113, 046401 (2014). Crossref, Google Scholar
    • 79. T. Meng and L. Balents, Phys. Rev. B 86, 054504 (2012). Crossref, Google Scholar
    • 80. T. Das, Phys. Rev. B 88, 035444 (2013). Crossref, Google Scholar
    • 81. J. D. Sau and S. Tewari, Phys. Rev. B 86, 104509 (2012). Crossref, Google Scholar
    • 82. D. Xiao, W. Yao and Q. Niu, Phys. Rev. Lett. 99, 236809 (2007). Crossref, Google Scholar
    • 83. C.-P. Chuu, M.-C. Chang and Q. Niu, Solid State Commun. 150, 533 (2010). Crossref, Google Scholar
    • 84. D. Culcer, Y. Yao and Q. Niu, Phys. Rev. B 72, 085110 (2005). Crossref, Google Scholar
    • 85. G. Sundaram and Q. Niu, Phys. Rev. B 59, 14915 (1999). Crossref, Google Scholar
    • 86. Y. Gao, S. A. Yang and Q. Niu, Phys. Rev. Lett. 112, 166601 (2014). Crossref, Google Scholar
    • 87. W. Yao, D. Xiao and Q. Niu, Phys. Rev. B 77, 235406 (2008). Crossref, Google Scholar
    • 88. T. Cai, S. A. Yang, X. Li, F. Zhang, J. Shi, W. Yao and Q. Niu, Phys. Rev. B 88, 115140 (2013). Crossref, Google Scholar
    • 89. K. F. Mak, K. He, J. Shan and T. F. Heinz, Nat. Nano 7, 494 (2012). Crossref, Google Scholar
    • 90. H. Zeng, J. Dai, W. Yao, D. Xiao and X. Cui, Nat. Nano 7, 490 (2012). Crossref, Google Scholar
    • 91. T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, B. Liu and J. Feng, Nat. Commun. 3, 887 (2012). Crossref, Google Scholar
    • 92. X. Xu, W. Yao, D. Xiao and T. F. Heinz, Nat. Phys. 10, 343 (2014). Crossref, Google Scholar
    • 93. K. F. Mak, K. L. McGill, J. Park and P. L. McEuen, Science 344, 1489 (2014). Crossref, Google Scholar
    • 94. A. Rycerz, J. Tworzydlo and C. W. J. Beenakker, Nat. Phys. 3, 172 (2007). Crossref, Google Scholar
    • 95. D. S. L. Abergel and T. Chakraborty, Appl. Phys. Lett. 95, 062107 (2009). Crossref, Google Scholar
    • 96. D. Gunlycke and C. T. White, Phys. Rev. Lett. 106, 136806 (2011). Crossref, Google Scholar
    • 97. Y. Jiang, T. Low, K. Chang, M. I. Katsnelson and F. Guinea, Phys. Rev. Lett. 110, 046601 (2013). Crossref, Google Scholar
    • 98. T. Fujita, M. B. A. Jalil and S. G. Tan, Appl. Phys. Lett. 97, 043508 (2010). Crossref, Google Scholar
    • 99. H. Pan, X. Li, H. Jiang, Y. Yao and S. A. Yang, Phys. Rev. B 91, 045404 (2015). Crossref, Google Scholar
    • 100. F. Zhang, J. Jung, G. A. Fiete, Q. Niu and A. H. MacDonald, Phys. Rev. Lett. 106, 156801 (2011). Crossref, Google Scholar
    • 101. H. Pan, Z. Li, C.-C. Liu, G. Zhu, Z. Qiao and Y. Yao, Phys. Rev. Lett. 112, 106802 (2014). Crossref, Google Scholar
    • 102. H. Pan, X. Li, F. Zhang and S. A. Yang, Phys. Rev. B 92, 041404 (2015). Crossref, Google Scholar
    • 103. I. Martin, Y. M. Blanter and A. F. Morpurgo, Phys. Rev. Lett. 100, 036804 (2008). Crossref, Google Scholar
    • 104. W. Yao, S. A. Yang and Q. Niu, Phys. Rev. Lett. 102, 096801 (2009). Crossref, Google Scholar
    • 105. H. Nielsen and M. Ninomiya, Phys. Lett. B 130, 389 (1983). Crossref, Google Scholar
    • 106. X. Huang, L. Zhao, Y. Long, P. Wang, D. Chen, Z. Yang, H. Liang, M. Xue, H. Weng, Z. Fang, X. Dai and G. Chen, Phys. Rev. X 5, 031023 (2015). Google Scholar
    • 107. C.-L. Zhang, S.-Y. Xu, I. Belopolski, Z. Yuan, Z. Lin, B. Tong, G. Bian, N. Alidoust, C.-C. Lee, S.-M. Huang, T.-R. Chang, G. Chang, C.-H. Hsu, H.-T. Jeng, M. Neupane, D. S. Sanchez, H. Zheng, J. Wang, H. Lin, C. Zhang, H.-Z. Lu, S.-Q. Shen, T. Neupert, M. Zahid Hasan and S. Jia, Nat. Commun. 7, 10735 (2016). Crossref, Google Scholar
    • 108. F. Arnold, C. Shekhar, S.-C. Wu, Y. Sun, R. D. Dos Reis, N. Kumar, M. Naumann, M. O. Ajeesh, M. Schmidt, A. G. Grushin, J. H. Bardarson, M. Baenitz, D. Sokolov, H. Borrmann, M. Nicklas, C. Felser, E. Hassinger and B. Yan, Nat. Commun. 7, 11615 (2016). Crossref, Google Scholar
    • 109. S. A. Yang, H. Pan and F. Zhang, Phys. Rev. Lett. 115, 156603 (2015). Crossref, Google Scholar
    • 110. Q.-D. Jiang, H. Jiang, H. Liu, Q.-F. Sun and X. C. Xie, Phys. Rev. Lett. 115, 156602 (2015). Crossref, Google Scholar
    • 111. F. I. Fedorov, Dokl. Akad. Nauk SSSR 105, 465 (1955). Google Scholar
    • 112. C. Imbert, Phys. Rev. D 5, 787 (1972). Crossref, Google Scholar
    • 113. M. Onoda, S. Murakami and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004). Crossref, Google Scholar
    • 114. J. Hellerstedt, M. T. Edmonds, N. Ramakrishnan, C. Liu, B. Weber, A. Tadich, K. M. ODonnell, S. Adam and M. S. Fuhrer, Nano Lett. 16, 3210 (2016). Crossref, Google Scholar
    • 115. H. Pan, M. Wu, Y. Liu and S. A. Yang, Sci. Rep. 5, 14639 (2015). Crossref, Google Scholar
    • 116. X. Xiao, Y. Liu, Z. Liu, G. Ai, S. A. Yang and G. Zhou, Appl. Phys. Lett. 108, 032403 (2016). Crossref, Google Scholar