Dirac cone

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] 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. Quantum mechanically, 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. Dirac points only occur as a feature of two-dimensional materials, a linear dispersion in three dimensions is called a Weyl point.[3] 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.[4] The massless fermions lead to various quantum Hall effects and ultra high carrier mobility.[5] Dirac cones were observed in 2009, using Angle-resolved photoemission spectroscopy on the graphite intercalation compound KC8.[6]

References

  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. ↑ 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.
  4. ↑ 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.
  5. ↑ "Two-dimensional Dirac materials: Structure, properties, and rarity". Phys.org. Retrieved May 25, 2016.
  6. ↑ 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.


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