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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 ...
The two bands touch at the zone corners (the K point in the Brillouin zone), where there is a zero density of states but no band gap. The graphene sheet thus displays a semimetallic (or zero-gap semiconductor) character. Two of the six Dirac points are independent, while the rest are equivalent by symmetry.
The Dirac points are six locations in momentum space on the edge of the Brillouin zone, divided into two non-equivalent sets of three points. These sets are labeled K and K'. These sets give graphene a valley degeneracy of =. In contrast, for traditional semiconductors, the primary point of interest is generally Γ, where momentum is zero. [60]
In physics, particularly special relativity, light-cone coordinates, introduced by Paul Dirac [1] and also known as Dirac coordinates, are a special coordinate system where two coordinate axes combine both space and time, while all the others are spatial.
The Dirac velocity gives the gradient of the dispersion at large momenta , is the mass of particle or object. In the case of massless Dirac matter, such as the fermionic quasiparticles in graphene or Weyl semimetals, the energy-momentum relation is linear,
Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case.
In quantum mechanics a state space is a separable complex Hilbert space.The dimension of this Hilbert space depends on the system we choose to describe. [1] [2] The different states that could come out of any particular measurement form an orthonormal basis, so any state vector in the state space can be written as a linear combination of these basis vectors.
The defining property for the gamma matrices to generate a Clifford algebra is the anticommutation relation {,} = + = ,where the curly brackets {,} represent the anticommutator, is the Minkowski metric with signature (+ − − −), and is the 4 × 4 identity matrix.