Mikkel H. Brynildsen: Towards spectral gaps in graphene in a weak magnetic field

We introduce a discrete tight-binding model for graphene, a monolayer of carbon atoms in a honeycomb lattice. This model, due to P. R. Wallace (1947), features a two-band dispersion relation with conical singularities at two points in the Brillouin zone, the so-called "Dirac cones" and "Dirac points".

Motivated by the Wallace-model, we consider a simplified situation, where the discrete zero-field Hamiltonian has a dispersion relation with a single Dirac-cone. We show that gaps open in the spectrum of the associated magnetic Hamiltonian, when a weak orthogonal constant magnetic field is incorporated by means of the "Peierls-substitution". This is joint work (in progress) with Horia Cornean and Ira Herbst.