← Mathematical compendium
Published equation contexts
1016
Why this formula appears here
Graphene sits at the top of the census not because its electrons move fast in any absolute sense — three million metres per second is still a tenth of a percent of the vacuum speed of light — but because their low-energy behaviour is relativistic in form rather than merely in name. Near the point where graphene’s conduction and valence bands touch, its electrons obey a two-dimensional version of the massless Dirac equation, with the Fermi velocity vF standing in for c . Mikhail Katsnelson, Konstantin Novoselov, and Andre Geim used that fact in 2006 to predict something the vacuum makes almost impossible to see: a chiral, massless particle hitting an electrostatic barrier head-on tunnels…
Read the full article-specific guide →
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (2)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 28 · Crossed Fields
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Graphene sits at the top of the census not because its electrons move fast in any absolute sense — three million metres per second is still a tenth of a percent of the vacuum speed of light — but because their low-energy behaviour is relativistic in form rather than merely in name. Near the point where graphene’s conduction and valence bands touch, its electrons obey a two-dimensional version of the massless Dirac equation, with the Fermi velocity vF standing in for c . Mikhail Katsnelson, Konstantin Novoselov, and Andre Geim used that fact in 2006 to predict something the vacuum makes almost impossible to see: a chiral, massless particle hitting an electrostatic barrier head-on tunnels…
Equation guide → ·
Article →Equation 57 · Crossed Fields
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Put the two numbers next to each other and the crystal stops being a curiosity and becomes a calibration. The best emergent-Lorentz window any measured crystal can show is of order one percent: a first-order drift anisotropy is a ten-percent effect at a tenth of the cone speed, and even graphene’s own Fermi velocity drifts by a factor of three as the Dirac point is approached. Our own vacuum is not merely somewhat better than that. Stefano Liberati’s review of Lorentz-invariance tests gives the best measured bound on a rotationally invariant electron Lorentz-violation coefficient as roughly one part in 10^{16} [ 10 ] — fourteen orders of magnitude tighter than the best window any measured…
Equation guide → ·
Article →