Towards spectral gaps in graphene in a weak magnetic field

Hamiltonians in Magnetic Fields

27 November 15:30 - 16:30

Mikkel H. Brynildsen - Aalborg University

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.
Rafael D. Benguria
Pontificia Universidad Católica de Chile
Arne Jensen
Aalborg University
Georgi Raikov
Pontificia Universidad Católica de Chile
Grigori Rozenblioum
Chalmers/University of Gothenburg
Jan Philip Solovej
University of Copenhagen