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Equation 26 · Every Crystal Has Its Own Speed of Light

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vFv_F

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vFv_F

Symbol v_F

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subscript

subscript

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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 vFv_F 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…
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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 vFv_F 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 through with perfect transmission, regardless of the barrier’s height or width — the opposite of ordinary tunneling, whose probability collapses as the barrier grows [ 5 ] . They were explicit about why nobody had ever seen the genuine effect. A real Klein paradox, for an actual relativistic electron, needs a potential drop of order its own rest-mass energy squeezed into a Compton wavelength — electric fields above 10^{16} volts per centimetre, far past anything a laboratory can sustain. In graphene the identical physics runs at the voltages and length scales of an ordinary chip.

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