Honeycomb structures in magnetic fields

Abstract

Abstract We consider the nearest-neighbour tight binding model of the honeycomb lattice in magnetic fields and discover surprizing new analytical results that fully explain fractal spectra and experimentally observed asymmetries in the density of states of molecular graphene. We describe a fractal Cantor spectrum for irrational magnetic flux through a honeycomb, and establish the existence of zero energy Dirac cones for each rational flux with fully explicit estimates on the cone angle. Our results give a substantially more refined description of subtleties in the de Haas–van Alphen and quantum Hall effects, and provide the first quantitative bounds on transport coefficients for the tight-binding model under disorder.