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]
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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.
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"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. Archived from the original on 22 August 2023. Retrieved 18 August 2023.
^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.
In physics, Diraccones are features that occur in some electronic band structures that describe unusual electron transport properties of materials like...
Paul Adrien Maurice Dirac OM FRS (/dɪˈræk/; 8 August 1902 – 20 October 1984) was an English mathematical and theoretical physicist who is considered to...
term Dirac matter refers to a class of condensed matter systems which can be effectively described by the Dirac equation. Even though the Dirac equation...
have similar electronic structures. Both have a Diraccone and linear electronic dispersion around the Dirac points. Both also have a quantum spin Hall effect...
graphyne has the potential for Diraccones on its double and triple bonded carbon atoms.[citation needed] Due to the Diraccones, the conduction and valence...
(2009). "Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Diraccone on the surface". Nature Physics. 5 (6): 438–442. Bibcode:2009NatPh...5...
has a topologically insulating ground-state. Topologically protected Diraccone surface states have been observed in Bismuth selenide and its insulating...
In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single...
and carrier density. Graphene's electronic band-structure (so-called Diraccone structure) was first visualized in this material. Weak anti-localization...
of a fermionic field is the Dirac field, which describes fermions with spin-1/2: electrons, protons, quarks, etc. The Dirac field can be described as either...
doi:10.1103/revmodphys.82.3045. S2CID 260682103. "Superconductors: Diraccones come in pairs". Advanced Institute for Materials Research. wpi-aimr.tohoku...
in WTe2 Diraccone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS A new form of Ca3P2 with a ring of Dirac nodes Leslie...
{\displaystyle \phi =\pi } on every surface resulting in a Diraccone (or more generally an odd number of Diraccones) on every surface and therefore making the boundary...
exceptional points was done by Woldemar Voigt in 1902 in a crystal. Diraccones Non-Hermitian quantum mechanics Bergholtz, Emil J.; Budich, Jan Carl;...
Graphene is a semimetal whose conduction and valence bands meet at the Dirac points, which are six locations in momentum space, the vertices of its hexagonal...
exhibits a double Diraccone, enabling Dirac fermions. A 30 meV gap separates the cones, which indicates the quantum Hall effect and massive Dirac fermions. Close...
dynamically and thermally stable, but also has distorted Diraccones. The direction-dependent cones are robust against external strain with tuneable Fermi...
frequencies (see the Fourier transform of the Dirac delta function, showing infinite frequency bandwidth that the Dirac delta function has), the impulse response...
Cava; M. Z. Hasan (2009). "Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in Bi 2Te 3 and Sb 2Te 3". Physical Review...
case can be simulated in single-layer materials like graphene near the Diraccones, where the eigenergies are given by E g r a p h e n e = ± 2 ν ℏ e B v...
resulting pairs ("duons") are zero-frequency excitations that emerge at the Diraccones of the crystal's spectrum. Fractionalization List of quasiparticles Mean-field...
as in graphene. Phagraphene: Graphene-like allotrope with distorted Diraccones. Prismane C8 is a theoretically predicted metastable carbon allotrope...
; Zhang, C.; Ma, Z. S.; Ang, L. K. (2017). "Valleytronics in merging Diraccones: All-electric-controlled valley filter, valve, and universal reversible...
(plasmons). Diraccones appeared in the plexcitons' two-dimensional band-structure. An external magnetic field created a gap between the cones when the system...
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