Dirac cone

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Brillouin zone in graphene
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.

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 crossing-point which electrons avoid,[4] 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.[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 potassium-graphite intercalation compound KC8.[8] and on several bismuth-based alloys.[9][10][7]

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]

See also[edit]


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  6. ^ "Two-dimensional Dirac materials: Structure, properties, and rarity". Phys.org. Retrieved 25 May 2016.
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  8. ^ 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.
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  21. ^ Lu, Ling; Fu, Liang; Joannopoulos, John D.; Soljačic, Marin (17 March 2013). "Weyl points and line nodes in gyroid photonic crystals" (PDF). Nature Photonics. Retrieved 2 March 2018.
  22. ^ 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.
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Further reading[edit]

  • 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.