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arXiv · 2607.17676

Lorentz-Covariant Landau Levels of Tilted Dirac Fermions in Nonuniform Fields

Sushmita Saha·Alestin Mawrie
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Abstract

We develop an analytical theory of Landau quantization for tilted anisotropic Dirac fermions in an exponentially decaying magnetic field. Using anisotropy scaling and a Lorentz transformation, we recast the laboratory-frame problem into the isotropic Dirac equation in the boosted frame, where the exponentially decaying magnetic-field problem admits an exact solution. Transforming the boosted-frame spectrum back to the laboratory frame yields an implicit quantization condition with an intrinsically energy-dependent guiding-center parameter. We identify the conditions for physically admissible states. We further show that the formalism recovers the known uniform-field spectrum of tilted anisotropic Dirac fermions in the appropriate limit. Our results extend the Lorentz-covariant treatment of tilted anisotropic Dirac fermions to an exponentially decaying magnetic field and reveal the energy-dependent guiding-center structure generated by the inverse transformation to the laboratory frame.

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Sushmita Saha, Alestin Mawrie. 2026-07-20. Lorentz-Covariant Landau Levels of Tilted Dirac Fermions in Nonuniform Fields. https://arxiv.org/abs/2607.17676

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