NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2013, 4 (4), P. 467–473
ON SPECTRAL GAPS IN GRAPHENE IN A WEAK CONSTANT MAGNETIC FIELD
M.H. Brynildsen – Aalborg University, Department of Mathematics, Aalborg, Denmark; mikkelhb@math.aau.dk
H. D. Cornean – Aalborg University, Department of Mathematics, Aalborg, Denmark; cornean@math.aau.dk
We present a mathematical introduction to a widely used discrete tight-binding model for graphene. We also introduce the “Peierls substitution,” modelling the Hamiltonian of a 2d crystal in a perpendicular uniform magnetic field in this setting. We consider a discrete single-cone Hamiltonian closely related to the (doublecone) graphene Hamiltonian. Finally, we announce in this paper a result concerning an opening of gaps in the spectrum of this single-cone Hamiltonian, when the Peierls phase-factor arises from a weak, but non-zero, external magnetic field. Full proofs will be given elsewhere.