Dirac cone

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.

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.

[10][11] Dirac cones were observed in 2008-2009, using angle-resolved photoemission spectroscopy (ARPES) on the potassium-graphite intercalation compound KC8[12] and on several bismuth-based alloys.

[13][14][11] 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.

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.
Tilted Dirac cones in momentum space. From left to right, the tilt increases, from no tilt in the first cone to overtilt in the last. The three first are Type-I Weyl semimetals, the last one is a Type-II Weyl semimetal.