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arXiv · 2505.04202

WKB energy levels in gapped graphene under crossed electromagnetic fields

I. O. Nimyi·S. G. Sharapov·V. P. Gusynin
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Abstract

We consider a single layer of graphene subjected to a magnetic field $H$ applied perpendicular to the layer and an in-plane constant radial electric field $E$. The Dirac equation for this configuration does not admit analytical solutions in terms of known special functions. Using the WKB approximation, we demonstrate that for gapped graphene the Bohr-Sommerfeld quantization condition for eigenenergies includes an additional valley-dependent geometrical phase. When this term is accounted for, the WKB approximation exhibits good agreement with results from the exact diagonalization method except to the lowest Landau level.

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I. O. Nimyi, S. G. Sharapov, V. P. Gusynin. 2025-05-07. WKB energy levels in gapped graphene under crossed electromagnetic fields. https://doi.org/10.1063/10.0036517

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