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.
Typical examples include graphene, topological insulators, bismuthantimonythin 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.
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.
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 momentumkx 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] In 2014, direct observation of the Dirac semimetal band structure using ARPES was conducted on the Dirac semimetal cadmium arsenide.[26][27][28]
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^Dirac cones could exist in bismuth–antimony films. Physics World, Institute of Physics, 17 April 2012.
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^ 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.
^ 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.
^ "Two-dimensional Dirac materials: Structure, properties, and rarity". Phys.org. Retrieved 25 May 2016.
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^ 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.
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^ 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. PMC4773426. PMID 26911701.
^ 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. PMC4895020. PMID 27241624.
^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.
^ 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.
^ 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.
^ 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. PMC4642520. PMID 26272041.
^ 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.
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dirac, cone, named, after, paul, dirac, features, that, occur, some, electronic, band, structures, that, describe, unusual, electron, transport, properties, materials, like, graphene, topological, insulators, these, materials, energies, near, fermi, level, val. 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 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 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 Contents 1 Description 2 Analog systems 3 See also 4 References 5 Further readingDescription edit nbsp 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 k x and k y However this concept can be extended to three dimensions where Dirac semimetals are defined by a linear dispersion relation between energy and k x k y and k z 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 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 editDirac points have been realized in many physical areas such as plasmonics phononics or nanophotonics microcavities 29 photonic crystals 30 See also editDirac matterReferences edit a b 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 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 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 Dirac cones could exist in bismuth antimony films Physics World Institute of Physics 17 April 2012 Hsieh David 2008 A topological Dirac insulator in a quantum spin Hall phase Nature 452 7190 970 974 Bibcode 2008Natur 452 970H doi 10 1038 nature06843 PMID 18432240 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 The Nobel Prize in Physics 2010 Press Release Nobelprize org 5 October 2010 Retrieved 2011 12 31 Fuchs Jean Noel 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 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 Two dimensional Dirac materials Structure properties and rarity Phys org Retrieved 25 May 2016 a b c 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 Gruneis 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 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 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 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 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 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 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 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 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 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 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 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 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 Lu Ling Fu Liang Joannopoulos John D Soljacic 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 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 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 Borisenko Sergey Gibson Quinn Evtushinsky Danil Zabolotnyy Volodymyr Buchner 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 Tercas 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 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 Further reading editWehling 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 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 Physics 8 84 Bibcode 2015PhyOJ 8 84V doi 10 1103 Physics 8 84 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 11 1140 1144 arXiv 1612 00416 Bibcode 2016NatMa 15 1140J doi 10 1038 nmat4787 PMID 27777402 S2CID 1115349 Hasan M Z Xu S Y Neupane M 2015 Chapter 4 Topological insulators topological Dirac semimetals topological crystalline insulators and topological Kondo insulators In Ortmann Frank Roche Stephan Valenzuela Sergio O eds Topological Insulators Fundamentals and Perspectives Wiley pp 55 100 arXiv 1406 1040 Bibcode 2014arXiv1406 1040Z ISBN 978 3 527 33702 6 nbsp This quantum mechanics related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Dirac cone amp oldid 1170989588, wikipedia, wiki, book, books, library,
