Dirac cone

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Electronic band structure of monolayer graphene. Zoom on the Dirac cones. There are 6 cones as the reciprocal lattice is also a honeycomb lattice.

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] 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[2] 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.[3] The massless fermions lead to various quantum Hall effects and ultra high carrier mobility.[4] Dirac cones were observed in 2009, using angle-resolved photoemission spectroscopy (ARPES) on the graphite intercalation compound KC8.[5]

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. 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.[6][7] In 2014, direct observation of the Dirac semimetal band structure using ARPES was conducted on the Dirac semimetal cadmium arsenide.[8]


  1. ^ "Superconductors: Dirac cones come in pairs". Tohoku University Advanced Institute for Materials Research - Research Highlights. 29 Aug 2011. Retrieved 2 Mar 2018.
  2. ^ Jean-Noël Fuchs; Lih-King Lim; Gilles Montambaux (2012). "Interband tunneling near the merging transition of Dirac cones" (PDF). 86. Physical Review A: 063613. arXiv:1210.3703. Bibcode:2012PhRvA..86f3613F. doi:10.1103/PhysRevA.86.063613.
  3. ^ 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)
  4. ^ "Two-dimensional Dirac materials: Structure, properties, and rarity". Phys.org. Retrieved May 25, 2016.
  5. ^ 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.CS1 maint: Uses authors parameter (link)
  6. ^ 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). doi:10.1038/ncomms11696. ISSN 2041-1723.
  7. ^ 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)
  8. ^ 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). doi:10.1103/PhysRevLett.113.027603. ISSN 0031-9007.