WKB energy levels in gapped graphene under crossed electromagnetic fields
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918012533080064 |
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| author | Nimyi, I. O. Sharapov, S. G. Gusynin, V. P. |
| author_facet | Nimyi, I. O. Sharapov, S. G. Gusynin, V. P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | WKB energy levels in gapped graphene under crossed electromagnetic fields Nimyi, I. O. Sharapov, S. G. Gusynin, V. P. Mesoscale and Nanoscale Physics 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. |
| title | WKB energy levels in gapped graphene under crossed electromagnetic fields |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2505.04202 |