Dirac cone

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.

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.

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]

  1. ^ 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.
  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.