Dirac cone

Dirac cones, named after Paul Dirac, are features that occur in some electronic band structures that describe unusual electron transport properties of materials like graphene and topological insulators.[1][2][3] In these materials, at energies near the Fermi level, the valence band and conduction band take the shape of the upper and lower halves of a conical surface, meeting at what are called Dirac points. In quantum mechanics, Dirac cones are a kind of avoided crossing[4] where the energy of the valence and conduction bands are not equal anywhere in two dimensional k-space except at the zero dimensional Dirac points. As a result of the cones, electrical conduction can be described by the movement of charge carriers which are massless fermions, a situation which is handled theoretically by the relativistic Dirac equation.[5] The massless fermions lead to various quantum Hall effects, magnetoelectric effects in topological materials, and ultra high carrier mobility.[6][7] Dirac cones were observed in 2008-2009, using angle-resolved photoemission spectroscopy (ARPES) on the graphite intercalation compound KC8.[8] and on several bismuth-based alloys.[9][10][7]

Electronic band structure of monolayer graphene. Zoom on the Dirac cones. There are 6 cones corresponding to the six vertices of the hexagonal first Brillouin zone.

As an object with three dimensions, Dirac cones are a feature of two-dimensional materials or surface states, based on a linear dispersion relation between energy and the two components of the crystal momentum kx and ky. However, this concept can be extended to three dimensions, where Dirac semimetals are defined by a linear dispersion relation between energy and kx, ky, and kz. In k-space, this shows up as a hypercone, which have doubly degenerate bands which also meet at Dirac points.[7] Dirac semimetals contain both time reversal and spatial inversion symmetry; when one of these is broken, the Dirac points are split into two constituent Weyl points, and the material becomes a Weyl semimetal. [11][12][13][14][15][16][17][18][19][20][21] In 2014, direct observation of the Dirac semimetal band structure using ARPES was conducted on the Dirac semimetal cadmium arsenide.[22][23][24]

Further reading
  • Wehling, T.O; Black-Schaffer, A.M; Balatsky, A.V (2014). "Dirac materials". Advances in Physics. 63 (1): 1. arXiv:1405.5774. doi:10.1080/00018732.2014.927109.
  • Johnston, Hamish (23 July 2015). "Weyl fermions are spotted at long last". Physics World. Retrieved 22 November 2018.
  • Ciudad, David (20 August 2015). "Massless yet real". Nature Materials. 14 (9): 863. doi:10.1038/nmat4411. ISSN 1476-1122. PMID 26288972.
  • Vishwanath, Ashvin (8 September 2015). "Where the Weyl Things Are". APS Physics. Retrieved 22 November 2018.
  • Jia, Shuang; Xu, Su-Yang; Hasan, M. Zahid (25 October 2016). "Weyl semimetals, Fermi arcs and chiral anomaly". Nature Materials. 15: 1140. arXiv:1612.00416. doi:10.1038/nmat4787.
  • Hasan, M. Z.; Xu, S.-Y.; Neupane, M. (2015). "4: Topological Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators". In Frank Ortmann; Stephan Roche; Sergio O. Valenzuela (eds.). Topological Insulators: Fundamentals and Perspectives. Wiley. pp. 55–100. arXiv:1406.1040. Bibcode:2014arXiv1406.1040Z. ISBN 978-3-527-33702-6.

References
  1. Novoselov, K.S.; Geim, A.K. (2007). "The rise of graphene". Nature Materials. 6: 183–191.
  2. Hasan, M.Z.; Kane, C.L. (2010). "Topological Insulators". Rev. Mod. Phys. 82: 3045. Bibcode:2010RvMP...82.3045H. doi:10.1103/revmodphys.82.3045.
  3. "Superconductors: Dirac cones come in pairs". Tohoku University Advanced Institute for Materials Research - Research Highlights. 29 Aug 2011. Retrieved 2 Mar 2018.
  4. Jean-Noël Fuchs; Lih-King Lim; Gilles Montambaux (2012). "Interband tunneling near the merging transition of Dirac cones" (PDF). Physical Review A. 86 (6): 063613. arXiv:1210.3703. Bibcode:2012PhRvA..86f3613F. doi:10.1103/PhysRevA.86.063613.
  5. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos & A. A. Firsov (10 Nov 2005). "Two-dimensional gas of massless Dirac fermions in graphene". Nature. Retrieved 2 Mar 2018.CS1 maint: multiple names: authors list (link)
  6. "Two-dimensional Dirac materials: Structure, properties, and rarity". Phys.org. Retrieved May 25, 2016.
  7. Hasan, M.Z.; Moore, J.E. (2011). "Three-Dimensional Topological Insulators". Annual Review of Condensed Matter Physics. 2: 55. arXiv:1011.5462. doi:10.1146/annurev-conmatphys-062910-140432.
  8. A. Grüneis, C. Attaccalite, A. Rubio, D. V. Vyalikh, S. L. Molodtsov, J. Fink, R. Follath, W. Eberhardt, B. Büchner, and T. Pichler (2009). "Angle-resolved photoemission study of the graphite intercalation compound KC8: A key to graphene". Physical Review B. 80 (7): 075431. Bibcode:2009PhRvB..80g5431G. doi:10.1103/PhysRevB.80.075431. hdl:10261/95912.CS1 maint: uses authors parameter (link)
  9. Hsieh, D.; Qian, D.; Wray, L.; Xia, Y.; Hor, Y. S.; Cava, R. J.; Hasan, M. Z. (2008). "A topological Dirac insulator in a quantum spin Hall phase". Nature. 452 (7190): 970–974. arXiv:0902.1356. Bibcode:2008Natur.452..970H. doi:10.1038/nature06843. ISSN 0028-0836. PMID 18432240.
  10. Hsieh, D.; Xia, Y.; Qian, D.; Wray, L.; Dil, J. H.; Meier, F.; Osterwalder, J.; Patthey, L.; Checkelsky, J. G.; Ong, N. P.; Fedorov, A. V.; Lin, H.; Bansil, A.; Grauer, D.; Hor, Y. S.; Cava, R. J.; Hasan, M. Z. (2009). "A tunable topological insulator in the spin helical Dirac transport regime". Nature. 460 (7259): 1101–1105. arXiv:1001.1590. Bibcode:2009Natur.460.1101H. doi:10.1038/nature08234. PMID 19620959.
  11. Wehling, T.O; Black-Schaffer, A.M; Balatsky, A.V (2014). "Dirac materials". Advances in Physics. 63 (1): 1. arXiv:1405.5774v1. doi:10.1080/00018732.2014.927109.
  12. Singh, Bahadur; Sharma, Ashutosh; Lin, H.; Hasan, M. Z.; Prasad, R.; Bansil, A. (2012-09-18). "Topological electronic structure and Weyl semimetal in the TlBiSe2 class". Physical Review B. 86 (11): 115208. arXiv:1209.5896. doi:10.1103/PhysRevB.86.115208.
  13. Huang, S.-M.; Xu, S.-Y.; Belopolski, I.; Lee, C.-C.; Chang, G.; Wang, B. K.; Alidoust, N.; Bian, G.; Neupane, M.; Zhang, C.; Jia, S.; Bansil, A.; Lin, H.; Hasan, M. Z. (2015). "A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class". Nature Communications. 6: 7373. Bibcode:2015NatCo...6.7373H. doi:10.1038/ncomms8373. PMC 4490374. PMID 26067579.
  14. Weng, Hongming; Fang, Chen; Fang, Zhong; Bernevig, B. Andrei; Dai, Xi (2015). "Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides". Physical Review X. 5 (1): 011029. arXiv:1501.00060. Bibcode:2015PhRvX...5a1029W. doi:10.1103/PhysRevX.5.011029.
  15. Xu, S.-Y.; Belopolski, I.; Alidoust, N.; Neupane, M.; Bian, G.; Zhang, C.; Sankar, R.; Chang, G.; Yuan, Z.; Lee, C.-C.; Huang, S.-M.; Zheng, H.; Ma, J.; Sanchez, D. S.; Wang, B. K.; Bansil, A.; Chou, F.-C.; Shibayev, P. P.; Lin, H.; Jia, S.; Hasan, M. Z. (2015). "Discovery of a Weyl Fermion semimetal and topological Fermi arcs". Science. 349 (6248): 613–617. arXiv:1502.03807. Bibcode:2015Sci...349..613X. doi:10.1126/science.aaa9297. PMID 26184916.
  16. Xu, Su-Yang; Alidoust, Nasser; Belopolski, Ilya; Yuan, Zhujun; Bian, Guang; Chang, Tay-Rong; Zheng, Hao; Strocov, Vladimir N.; Sanchez, Daniel S.; Chang, Guoqing; Zhang, Chenglong et.al., (2015). "Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide". Nature Physics. 11 (9): 748–754. arXiv:1504.01350. doi:10.1038/nphys3437. ISSN 1745-2481.CS1 maint: extra punctuation (link)
  17. Huang, Xiaochun; Zhao, Lingxiao; Long, Yujia; Wang, Peipei; Chen, Dong; Yang, Zhanhai; Liang, Hui; Xue, Mianqi; Weng, Hongming; Fang, Zhong; Dai, Xi; Chen, Genfu (2015). "Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal Ta As". Physical Review X. 5 (3): 031023. arXiv:1503.01304. Bibcode:2015PhRvX...5c1023H. doi:10.1103/PhysRevX.5.031023.
  18. Zhang, Cheng-Long; Xu, Su-Yang; Belopolski, Ilya; Yuan, Zhujun; Lin, Ziquan; Tong, Bingbing; Bian, Guang; Alidoust, Nasser; Lee, Chi-Cheng; Huang, Shin-Ming; Chang, Tay-Rong et.al., (2016-02-25). "Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl fermion semimetal". Nature Communications. 7 (1): 1–9. doi:10.1038/ncomms10735. ISSN 2041-1723.CS1 maint: extra punctuation (link)
  19. Schoop, Leslie M.; Ali, Mazhar N.; Straßer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; Duppel, Viola; Parkin, Stuart S. P.; Lotsch, Bettina V.; Ast, Christian R. (2016). "Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS". Nature Communications. 7 (1): 11696. arXiv:1509.00861. doi:10.1038/ncomms11696. ISSN 2041-1723. PMC 4895020. PMID 27241624.
  20. Neupane, M.; Belopolski, I.; Hosen, Md. M; Sanchez, D.S.; Sankar, R.; Szlawska, M.; Xu, S.-X.; Dimitri, K.; Dhakal, N.; Maldonado, P.; Oppeneer, P.; Kaczorowski, D.; Chou, F.; Hasan, M.Z.; Durakiewicz, T. (2016). "Observation of topological nodal fermion semimetal phase in ZrSiS". Phys. Rev. B. 93 (20): 201104(R). arXiv:1604.00720v1. doi:10.1103/PhysRevB.93.201104. ISSN 2469-9969.
  21. Ling Lu, Liang Fu, John D. Joannopoulos and Marin Soljacˇic (17 Mar 2013). "Weyl points and line nodes in gyroid photonic crystals" (PDF). Nature Photonics. Retrieved 2 Mar 2018.CS1 maint: multiple names: authors list (link)
  22. Neupane, Madhab; Xu, Su-Yang; Sankar, Raman; Nasser, Alidoust; Bian, Guang; Liu, Chang; Belopolski, Ilya; Chang, Tay-Rong; Jeng, Horng-Tay; Lin, Hsin; Bansil, Aron; Chou, Fang-Cheng; Hasan, M. Zahid (2014). "Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2". Nature Communications. 5: 3786. Bibcode:2014NatCo...5E3786N. doi:10.1038/ncomms4786.
  23. Sankar, R.; Neupane, M.; Xu, S.-Y.; Butler, C. J.; Zeljkovic, I.; Panneer Muthuselvam, I.; Huang, F.-T.; Guo, S.-T.; Karna, Sunil K.; Chu, M.-W.; Lee, W. L.; Lin, M.-T.; Jayavel, R.; Madhavan, V.; Hasan, M. Z.; Chou, F. C. (2015). "Large single crystal growth, transport property, and spectroscopic characterizations of three-dimensional Dirac semimetal Cd3As2". Scientific Reports. 5: 12966. Bibcode:2015NatSR...512966S. doi:10.1038/srep12966. PMC 4642520. PMID 26272041.
  24. Borisenko, Sergey; Gibson, Quinn; Evtushinsky, Danil; Zabolotnyy, Volodymyr; Büchner, Bernd; Cava, Robert J. (2014). "Experimental Realization of a Three-Dimensional Dirac Semimetal". Physical Review Letters. 113 (2): 027603. arXiv:1309.7978. Bibcode:2014PhRvL.113b7603B. doi:10.1103/PhysRevLett.113.027603. ISSN 0031-9007. PMID 25062235.


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.