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arXiv · 2010.14328

Graphene on noncommutative plane and the Seiberg-Witten map

Aslam Halder
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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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Aslam Halder. 2020-10-27. Graphene on noncommutative plane and the Seiberg-Witten map. https://arxiv.org/abs/2010.14328

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