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Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime

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Abstract

In this paper, we analyze the relativistic and nonrelativistic energy spectra (fermionic Landau levels) for the noncommutative quantum Hall effect with anomalous magnetic moment in the conical Gödel-type spacetime in \((2+1)\)-dimensions, where such spacetime is the combination of the flat Gödel-type spacetime with a cosmic string (conical gravitational topological defect). To analyze these energy spectra, we start from the noncommutative Dirac equation with minimal and nonminimal couplings in polar coordinates. Using the tetrads formalism, we obtain a second-order differential equation. Next, we solve exactly this differential equation, where we obtain a generalized Laguerre equation, and also a quadratic polynomial equation for the total relativistic energy. By solving this polynomial equation, we obtain the relativistic energy spectrum of the fermion and antifermion. Besides, we also analyze the nonrelativistic limit of the system, where we obtain the nonrelativistic energy spectrum. In both cases (relativistic and nonrelativistic), we discuss in detail the characteristics of each spectrum as well as the influence of all parameters and physical quantities in such spectra. Comparing our problem with other works, we verified that our results generalize several particular cases in the literature.

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This manuscript has no associated data or the data will not be deposited. [Author’s comment: There is no data because this is theoretical work based on calculations to obtain the relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Godel-type spacetime.]

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Acknowledgements

The author would like to thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for financial support.

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  1. Departamento de Física, Universidade Federal do Ceará (UFC), Campus do Pici, Fortaleza, CE, C.P. 6030, 60455-760, Brazil

    R. R. S. Oliveira

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Oliveira, R.R.S. Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime. Gen Relativ Gravit 56, 30 (2024). https://doi.org/10.1007/s10714-024-03209-9

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