Carbon Hybridization to Tight-Binding to Dirac Solid – TheWonder Laboratory of Graphene
We make a pedagogical survey on why the charge carriers(electrons) in graphene are called massless Dirac fermions.Our analysis begins at the beginning, namely, we start fromthe quantum chemistry of two nearby carbon (C) atoms andshow how their hybridized orbitals ‘valence-bond’ with eachother to form an energy-band in the solid-state. This yieldsa two-dimensional honeycomb lattice of graphene, which canbe viewed as two inter-penetrating triangular sublattices. Thatrecognition provides a perfect setting for describing the dynamicsof the last weakly-localized valence electron of C ina tight-binding model, which captures all the unusual electronicphenomena of graphene. The latter emerges from aresemblance to the relativistic Dirac theory of electrons because,in the long-wavelength limit, the energy dispersion islinear in the wave vector. We build up – step by step – this remarkabletransition of a carbon-based material to an exotictwo-dimensional Dirac solid, in which much of the quantumaspects of modern condensed matte physics can be tested inthe laboratory.
Volume 25 | Issue 5