WKB energy levels in gapped graphene under crossed electromagnetic fields
Mesoscale and Nanoscale Physics
2025-05-08 v1
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.
Keywords
Cite
@article{arxiv.2505.04202,
title = {WKB energy levels in gapped graphene under crossed electromagnetic fields},
author = {I. O. Nimyi and S. G. Sharapov and V. P. Gusynin},
journal= {arXiv preprint arXiv:2505.04202},
year = {2025}
}
Comments
8 pages, 3 figures