Dirac cone
/ dee-RAHK KOHN /
Picture two ice-cream cones, one pointing up and one pointing down, touching tip to tip at a single point. If you make a chart of how much energy an electron has versus how fast it is moving, the electrons in graphene trace out exactly this double-cone shape. That picture is called a Dirac cone, and it explains why graphene's electrons are so strange.
A Dirac cone is a special pattern in a material's energy bands where the band of filled electron states and the band of empty states meet at a single point and rise away from it as straight slopes, like the sides of a cone, rather than the gentle curve found in ordinary materials. In most crystals an electron's energy grows as the square of its speed, which gives it an apparent mass; but along a straight-sided cone the energy grows in direct proportion to momentum — the same relationship light obeys (E = pc). Electrons living near such a point therefore behave as if they had no mass, zipping along at a single fixed speed regardless of their energy.
Dirac cones matter because they hand us, inside an ordinary chip-friendly material, electrons that mimic massless particles, giving graphene its blazing speed and unusual response to magnetic fields, and they are a hallmark of topological materials too. The honest caveat is that these electrons are not literally massless particles from outer space — they are ordinary electrons whose collective behavior in the crystal merely mimics masslessness, an analogy that holds only for energies close to the cone's tip.
When physicists used ARPES to photograph graphene's energy bands directly, the data formed a clean X-shape — the side view of a Dirac cone — with the filled and empty bands meeting at a single sharp point, the visible signature of its massless electrons.
Photographed directly, graphene's bands form an X — the side view of a Dirac cone.
The 'Dirac' name comes from the equation Paul Dirac wrote for fast-moving relativistic electrons, whose straight energy-versus-speed relation the cone reproduces — a striking case of high-energy physics reappearing, in disguise, inside an everyday sheet of carbon.