Dirac cone

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Electronic band structure of monolayer graphene, with a zoomed inset showing the Dirac cones. There are 6 cones corresponding to the 6 vertices of the hexagonal first Brillouin zone. Graphene Brillouin Zone & Linear Dispersion.PNG
Electronic band structure of monolayer graphene, with a zoomed inset showing the Dirac cones. There are 6 cones corresponding to the 6 vertices of the hexagonal first Brillouin zone.

In physics, Dirac cones 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.

Contents

Typical examples include graphene, topological insulators, bismuth antimony thin films and some other novel nanomaterials, [1] [4] [5] in which the electronic energy and momentum have a linear dispersion relation such that the electronic band structure near the Fermi level takes the shape of an upper conical surface for the electrons and a lower conical surface for the holes. The two conical surfaces touch each other and form a zero-band gap semimetal.

The name of Dirac cone comes from the Dirac equation that can describe relativistic particles in quantum mechanics, proposed by Paul Dirac. Isotropic Dirac cones in graphene were first predicted by P. R. Wallace in 1947 [6] and experimentally observed by the Nobel Prize laureates Andre Geim and Konstantin Novoselov in 2005. [7]

Description

Tilted Dirac cones in momentum space. From left to right, the tilt increases, from no tilt in the first cone to overtilt in the last. The three first are Type-I Weyl semimetals, the last one is a Type-II Weyl semimetal. Tilted dirac cones.png
Tilted Dirac cones in momentum space. From left to right, the tilt increases, from no tilt in the first cone to overtilt in the last. The three first are Type-I Weyl semimetals, the last one is a Type-II Weyl semimetal.

In quantum mechanics, Dirac cones are a kind of crossing-point which electrons avoid, [8] where the energy of the valence and conduction bands are not equal anywhere in two dimensional lattice 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. [9] The massless fermions lead to various quantum Hall effects, magnetoelectric effects in topological materials, and ultra high carrier mobility. [10] [11] Dirac cones were observed in 2008-2009, using angle-resolved photoemission spectroscopy (ARPES) on the potassium-graphite intercalation compound KC8 [12] and on several bismuth-based alloys. [13] [14] [11]

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. [11] 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. [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [ excessive citations ] In 2014, direct observation of the Dirac semimetal band structure using ARPES was conducted on the Dirac semimetal cadmium arsenide. [26] [27] [28]

Analog systems

Dirac points have been realized in many physical areas such as plasmonics, phononics, or nanophotonics (microcavities, [29] photonic crystals [30] ).

See also

References

  1. 1 2 Novoselov, K.S.; Geim, A.K. (2007). "The rise of graphene". Nature Materials. 6 (3): 183–191. Bibcode:2007NatMa...6..183G. doi:10.1038/nmat1849. PMID   17330084. S2CID   14647602.
  2. ↑ Hasan, M.Z.; Kane, C.L. (2010). "Topological Insulators". Rev. Mod. Phys. 82 (4): 3045. arXiv: 1002.3895 . Bibcode:2010RvMP...82.3045H. doi:10.1103/revmodphys.82.3045. S2CID   16066223.
  3. ↑ "Superconductors: Dirac cones come in pairs". Advanced Institute for Materials Research. wpi-aimr.tohoku.ac.jp. Research Highlights. Tohoku University. 29 August 2011. Retrieved 2 March 2018.
  4. ↑ Dirac cones could exist in bismuth–antimony films. Physics World, Institute of Physics, 17 April 2012.
  5. ↑ Hsieh, David (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. PMID   18432240. Archived from the original on 22 August 2023. Retrieved 18 August 2023.
  6. ↑ Wallace, P. R. (1947). "The Band Theory of Graphite". Physical Review. 71 (9): 622–634. Bibcode:1947PhRv...71..622W. doi:10.1103/PhysRev.71.622.
  7. ↑ The Nobel Prize in Physics 2010 Press Release. Nobelprize.org, 5 October 2010. Retrieved 2011-12-31.
  8. ↑ Fuchs, Jean-Noël; Lim, Lih-King; Montambaux, Gilles (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. S2CID   67850936. Archived from the original (PDF) on 21 January 2023. Retrieved 29 August 2018.
  9. ↑ Novoselov, K.S.; Geim, A.K.; Morozov, S.V.; Jiang, D.; Katsnelson, M.I.; Grigorieva, I.V.; et al. (10 November 2005). "Two-dimensional gas of massless Dirac fermions in graphene". Nature. 438 (7065): 197–200. arXiv: cond-mat/0509330 . Bibcode:2005Natur.438..197N. doi:10.1038/nature04233. PMID   16281030. S2CID   3470761 . Retrieved 2 March 2018.
  10. ↑ "Two-dimensional Dirac materials: Structure, properties, and rarity". Phys.org. Retrieved 25 May 2016.
  11. 1 2 3 Hasan, M.Z.; Moore, J.E. (2011). "Three-dimensional topological insulators". Annual Review of Condensed Matter Physics. 2: 55–78. arXiv: 1011.5462 . Bibcode:2011ARCMP...2...55H. doi:10.1146/annurev-conmatphys-062910-140432. S2CID   11516573.
  12. ↑ Grüneis, A.; Attaccalite, C.; Rubio, A.; Vyalikh, D.V.; Molodtsov, S.L.; Fink, J.; et al. (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 .
  13. ↑ 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. S2CID   4402113.
  14. ↑ Hsieh, D.; Xia, Y.; Qian, D.; Wray, L.; Dil, J.H.; Meier, F.; et al. (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. S2CID   4369601.
  15. ↑ Wehling, T.O.; Black-Schaffer, A.M.; Balatsky, A.V. (2014). "Dirac materials". Advances in Physics. 63 (1): 1. arXiv: 1405.5774 . Bibcode:2014AdPhy..63....1W. doi:10.1080/00018732.2014.927109. S2CID   118557449.
  16. ↑ Singh, Bahadur; Sharma, Ashutosh; Lin, H.; Hasan, M.Z.; Prasad, R.; Bansil, A. (18 September 2012). "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. S2CID   119109505.
  17. ↑ Huang, S.-M.; Xu, S.-Y.; Belopolski, I.; Lee, C.-C.; Chang, G.; Wang, B.K.; et al. (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.
  18. ↑ Weng, Hongming; Fang, Chen; Fang, Zhong; Bernevig, B. Andrei; Dai, Xi (2015). "Weyl semimetal phase in non-centrosymmetric transition-metal monophosphides". Physical Review X. 5 (1) 011029. arXiv: 1501.00060 . Bibcode:2015PhRvX...5a1029W. doi:10.1103/PhysRevX.5.011029. S2CID   15298985.
  19. ↑ Xu, S.-Y.; Belopolski, I.; Alidoust, N.; Neupane, M.; Bian, G.; Zhang, C.; et al. (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. S2CID   206636457.
  20. ↑ Xu, Su-Yang; Alidoust, Nasser; Belopolski, Ilya; Yuan, Zhujun; Bian, Guang; Chang, Tay-Rong; et al. (2015). "Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide". Nature Physics. 11 (9): 748–754. arXiv: 1504.01350 . Bibcode:2015NatPh..11..748X. doi:10.1038/nphys3437. ISSN   1745-2481. S2CID   119118252.
  21. ↑ Huang, Xiaochun; Zhao, Lingxiao; Long, Yujia; Wang, Peipei; Chen, Dong; Yang, Zhanhai; et al. (2015). "Observation of the chiral-anomaly-induced negative magnetoresistance in 3‑D Weyl semimetal TaAs". Physical Review X. 5 (3) 031023. arXiv: 1503.01304 . Bibcode:2015PhRvX...5c1023H. doi:10.1103/PhysRevX.5.031023. S2CID   55929760.
  22. ↑ Zhang, Cheng-Long; Xu, Su-Yang; Belopolski, Ilya; Yuan, Zhujun; Lin, Ziquan; Tong, Bingbing; et al. (25 February 2016). "Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl fermion semimetal". Nature Communications. 7 (1) 10735. arXiv: 1601.04208 . Bibcode:2016NatCo...710735Z. doi: 10.1038/ncomms10735 . ISSN   2041-1723. PMC   4773426 . PMID   26911701.
  23. ↑ Schoop, Leslie M.; Ali, Mazhar N.; Straßer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; et al. (2016). "Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS". Nature Communications. 7 (1) 11696. arXiv: 1509.00861 . Bibcode:2016NatCo...711696S. doi:10.1038/ncomms11696. ISSN   2041-1723. PMC   4895020 . PMID   27241624.
  24. ↑ Neupane, M.; Belopolski, I.; Hosen, Md.M.; Sanchez, D.S.; Sankar, R.; Szlawska, M.; et al. (2016). "Observation of topological nodal fermion semimetal phase in ZrSiS". Physical Review B. 93 (20): 201104(R). arXiv: 1604.00720 . Bibcode:2016PhRvB..93t1104N. doi:10.1103/PhysRevB.93.201104. ISSN   2469-9969. S2CID   118446447.
  25. ↑ Lu, Ling; Fu, Liang; Joannopoulos, John D.; Soljačic, Marin (17 March 2013). "Weyl points and line nodes in gyroid photonic crystals" (PDF). Nature Photonics. 7 (4): 294–299. arXiv: 1207.0478 . Bibcode:2013NaPho...7..294L. doi:10.1038/nphoton.2013.42. S2CID   5144108 . Retrieved 2 March 2018.
  26. ↑ Neupane, Madhab; Xu, Su-Yang; Sankar, Raman; Nasser, Alidoust; Bian, Guang; Liu, Chang; et al. (2014). "Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2". Nature Communications. 5: 3786. arXiv: 1309.7892 . Bibcode:2014NatCo...5.3786N. doi: 10.1038/ncomms4786 . PMID   24807399.
  27. ↑ Sankar, R.; Neupane, M.; Xu, S.-Y.; Butler, C.J.; Zeljkovic, I.; Panneer Muthuselvam, I.; et al. (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.
  28. ↑ 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. S2CID   19882802.
  29. ↑ Terças, H.; Flayac, H.; Solnyshkov, D. D.; Malpuech, G. (11 February 2014). "Non-Abelian Gauge Fields in Photonic Cavities and Photonic Superfluids". Physical Review Letters. 112 (6) 066402. arXiv: 1303.4286 . Bibcode:2014PhRvL.112f6402T. doi:10.1103/PhysRevLett.112.066402. PMID   24580697. S2CID   10674352.
  30. ↑ He, Wen-Yu; Chan, C. T. (2 February 2015). "The Emergence of Dirac points in Photonic Crystals with Mirror Symmetry". Scientific Reports. 5 (1): 8186. arXiv: 1409.3939 . Bibcode:2015NatSR...5E8186H. doi:10.1038/srep08186. ISSN   2045-2322. PMC   4650825 . PMID   25640993.

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