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

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. In 2014, direct observation of the Dirac
semimetal band structure using ARPES was conducted on the Dirac
semimetal cadmium arsenide.


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Original Article: http://en.wikipedia.org/wiki/Dirac_cone


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