Graphene on noncommutative plane and the Seiberg-Witten map

• URL: http://arxiv.org/abs/2010.14328v1
• Date: Tue, 27 Oct 2020 14:39:15 GMT
• Title: Graphene on noncommutative plane and the Seiberg-Witten map
• Authors: Aslam Halder
• Abstract summary: We study the quantum dynamics of a massless relativistic electron moves on monolayer graphene, in the presence of a constant background magnetic field, on NC plane. We also compute the energy spectrum of the NC Landau system in graphene. Interestingly, in this case helicity is found to be $theta$ modified.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graphene on two dimensional (2D) noncommutative (NC) plane in the presence of a constant background magnetic field has been studied. To handel the gauge-invariance issue we start our analysis by a effective massles NC Dirac field theory where we incorporate the Seiberg-Witten (SW) map along with the Moyal star ($\star$) product. The gauge-invariant Hamiltonian of a massless Dirac particle is then computed which is used to study the relativistic Landau problem of graphene on NC plane. Specifically we study the quantum dynamics of a massless relativistic electron moves on monolayer graphene, in the presence of a constant background magnetic field, on NC plane. We also compute the energy spectrum of the NC Landau system in graphene. The results obtained are corrected by the spatial NC parameter $\theta$. Finally we visit the Weyl equation for electron in graphene on NC plane. Interestingly, in this case helicity is found to be $\theta$ modified.

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