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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
mathematics
Graphene and non-Abelian quantization
Journal of Physics A: Mathematical and Theoretical, Volume 45, No. 13, Article 135308, Year 2012
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Description
In this paper, we employ a simple nonrelativistic model to describe the low energy excitation of graphene. The model is based on a deformation of the Heisenberg algebra which makes the commutator of momenta proportional to the pseudo-spin. We solve the Landau problem for the resulting Hamiltonian, which reduces in the large mass limit while keeping the Fermi velocity fixed, to the usual linear one employed to describe these excitations as massless Dirac fermions. This model, extended to negative mass, allows us to reproduce the leading terms in the low energy expansion of the dispersion relation for both nearest and next-to-nearest-neighbor interactions. Taking into account the contributions of both Dirac points, the resulting Hall conductivity, evaluated with a ζ-function approach, is consistent with the anomalous integer quantum Hall effect found in graphene. Moreover, when considered in first order perturbation theory, it is shown that the next-to-leading term in the interaction between nearest neighbor produces no modifications in the spectrum of the model while an electric field perpendicular to the magnetic field produces just a rigid shift of this spectrum. © 2012 IOP Publishing Ltd.
Authors & Co-Authors
Falomir, Horacio Alberto
Argentina, Buenos Aires
Consejo Nacional de Investigaciones Científicas y Técnicas
Gamboa, Jorge
Chile, Santiago
Pontificia Universidad Católica de Chile
Chile, Santiago
Universidad de Santiago de Chile
Loewe, M.
Chile, Santiago
Pontificia Universidad Católica de Chile
South Africa, Cape Town
University of Cape Town
Nieto, M.
Argentina, Buenos Aires
Consejo Nacional de Investigaciones Científicas y Técnicas
Statistics
Citations: 17
Authors: 4
Affiliations: 4
Identifiers
Doi:
10.1088/1751-8113/45/13/135308
ISSN:
17518113
e-ISSN:
17518121