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Spectral gaps in tight-binding graphene in a weak magnetic field

Mikkel Brynildsen
(Aalborg Universitet)
Math/Phys Seminar
Thursday, 15 August, 2013, at 15:15-16:15, in Aud. D4 (1531-219)
Abstract:
We introduce a discrete tight-binding model for graphene, a one atom thick flat carbon crystal of infinite extension. This model, due to Wallace (1947), features a two-band spectrum with conical singularities at two non-equivalent points in the Brillouin zone, the so-called "Dirac
cones" and "Dirac points".

The question is: What happens when an external weak magnetic field is imposed onto the infinite crystal of a material with one or more Dirac cones in the dispersion relation? (The external magnetic field being: constant in time, isotropic and perpendicular to the graphene lattice)

Motivated by the Wallace graphene spectrum, we consider a simplified situation, where the discrete zero-magnetic-field Hamiltonian has a two-band spectrum  with a single Dirac-cone. We show that gaps open in the spectrum of the associated magnetic Hamiltonian, when the external magnetic field is incorporated by means of the "Peierls-substitution". This simple model can be extended to the tight-binding graphene model with two Dirac-cones subjected to the external magnetic field via "Peierls-substitution".

This is joint work with Horia Cornean and Ira Herbst.
Contact person: Jacob Schach Møller