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The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios

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Abstract

In the present paper, we investigate the bound-state solutions of the noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios, namely: the Minkowski spacetime (inertial flat case), the spinning cosmic string (CS) spacetime (inertial curved case), and the spinning CS spacetime with noninertial effects (noninertial curved case). In particular, in the first two scenarios, we have an inertial frame, while in the third, we have a rotating frame. With respect to bound-state solutions, we focus primarily on eigenfunctions (Dirac spinor and wave function) and on energy eigenvalues (Landau levels), where we use the flat and curved Dirac equation in polar coordinates to reach such solutions. However, unlike the literature, here we consider a CS with a non-null angular momentum and also the NC of the positions, and therefore, we seek a more general description for the QHE. Once the solutions are obtained, we discuss the influence of all parameters and physical quantities on relativistic energy levels. Finally, we analyze the nonrelativistic limit, and we also compared our problem with other works, where we verified that our results generalize some particular cases of the literature.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Author’s comment: There is no data because this is a theoretical work based on calculations to describe the bound-state solutions of the NCQHE with AMM in three different relativistic scenarios, namely: the Minkowski spacetime (inertial flat case), the spinning CS spacetime (inertial curved case), and the spinning CS spacetime with noninertial effects (noninertial curved case).]

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Acknowledgements

The authors would like to thank the Fundação Cearense de Apoio ao Desenvolvimento Científico e Tecnológico (FUNCAP), the Coordenação de Aperfeiç oamento de Pessoal de Nível Superior (CAPES), and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for financial support.

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    R. R. S. Oliveira, G. Alencar & R. R. Landim

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Oliveira, R.R.S., Alencar, G. & Landim, R.R. The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios. Gen Relativ Gravit 55, 15 (2023). https://doi.org/10.1007/s10714-022-03057-5

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