WKB energy levels in gapped graphene under crossed electromagnetic fields
arXiv:2505.04202 · doi:10.1063/10.0036517
Abstract
We consider a single layer of graphene subjected to a magnetic field applied perpendicular to the layer and an in-plane constant radial electric field . 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.
8 pages, 3 figures
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