On spectral gaps in graphene in a weak constant magnetic field
Abstract
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.
Supporting agencies: TheauthorsacknowledgepartialsupportfromtheDanishFNUgrantMathematical Analysis of Many-Body Quantum Systems. The authors wish to thank the organizers of the conference Mathematical Challenge of Quantum Transport in Nanosystems, St. Petersburg, 2013.
About the Authors
M. Н. Brynildsen
Aalborg University, Department of Mathematics
Denmark
Denmark
Mikkel H. Brynildsen
Aalborg
H. D. Cornean
Aalborg University, Department of Mathematics
Denmark
Denmark
Horia D. Cornean
Aalborg
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Review
For citations:
Brynildsen M.Н., Cornean H.D. On spectral gaps in graphene in a weak constant magnetic field. Nanosystems: Physics, Chemistry, Mathematics. 2013;4(4):467-473.
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