Geodesic
On spectral gaps in graphene in a weak constant magnetic field
Nanosistemy: fizika, himiâ, matematika, Tome 4 (2013) no. 4, pp. 467-473

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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 (doublecone) 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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     author = {M. H. Brynildsen and H. D. Cornean},
     title = {On spectral gaps in graphene in a weak constant magnetic field},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {467--473},
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     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2013_4_4_a1/}
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M. H. Brynildsen; H. D. Cornean. On spectral gaps in graphene in a weak constant magnetic field. Nanosistemy: fizika, himiâ, matematika, Tome 4 (2013) no. 4, pp. 467-473. http://geodesic.mathdoc.fr/item/NANO_2013_4_4_a1/