Critical Mass in Graphene

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Science  21 Jun 2013:
Vol. 340, Issue 6139, pp. 1413-1414
DOI: 10.1126/science.1240317

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One of the most striking properties of graphene, a single-atom-thick layer of carbon, is that the electrons behave as if they have no mass. They move at a constant velocity, regardless of their energy, much like photons, the more familiar massless particles of light. Special relativity tells us that a minimum energy E = 2m0c2 is required to create a particle and antiparticle of rest mass m0 (c is the speed of light; the 2 occurs because two particles are created). Because photons have no rest mass, a pair of photons can be created with energies all the way down to zero energy. In a solid, the band gap energy Eg = 2m0v2 is the energy required to create an electron and hole (particle and antiparticle), where m0 is the effective mass and v is the Fermi velocity (typically less than the speed of light by a factor of several hundred). Thus, mass and band gap are intimately related; no mass equates to no band gap, and until now that was the end of the story in graphene. On page 1427 of this issue, Hunt et al. (1) show that electrons in graphene can gain a mass under the right circumstances.