ON SPECTRAL GAPS IN GRAPHENE IN A WEAK CONSTANT MAGNETIC FIELD
Аннотация:
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 (double- cone) 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.
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