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PreprintCC BY 4.0arXiv

Energy levels of screened charged impurity in gapped graphene under magnetic field

  • Andrii Iurov
  • V. P. Gusynin
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Abstract

In this paper, we present a comprehensive theoretical study of the electronic states in gapped graphene in the presence of a charge impurity and a magnetic field. We focus on the impurity-induced modification of the Landau levels under the influence of an attractive or repulsive Coulomb potential. Since analytical solutions of the Dirac equation are not available in this case, the study is carried out using the Wentzel-Kramers-Brillouin (WKB) approach. Special attention is paid to the screening of the Coulomb potential in the presence of metallic gates situated at some distances from graphene sheet, as is commonly the case in experiments. Using both analytical and numerical methods, we determine the energy spectrum as a function of the magnetic field strength and impurity charge for screened and unscreened Coulomb potentials. Our results reveal a significant dependence of the energy levels for sample-to-gate distances of less than 50 nm.

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Cite

BibTeXRIS
BibTeX
@misc{iurov2026energy,
  title = {{Energy levels of screened charged impurity in gapped graphene under magnetic field}},
  author = {Andrii Iurov and V. P. Gusynin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17492},
  eprint = {2610.17492},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17492},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Energy levels of screened charged impurity in gapped graphene under magnetic field
AU  - Andrii Iurov
AU  - V. P. Gusynin
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17492
UR  - https://arxiv.org/abs/2610.17492
AB  - In this paper, we present a comprehensive theoretical study of the electronic states in gapped graphene in the presence of a charge impurity and a magnetic field. We focus on the impurity-induced modification of the Landau levels under the influence of an attractive or repulsive Coulomb potential. Since analytical solutions of the Dirac equation are not available in this case, the study is carried out using the Wentzel-Kramers-Brillouin (WKB) approach. Special attention is paid to the screening of the Coulomb potential in the presence of metallic gates situated at some distances from graphene sheet, as is commonly the case in experiments. Using both analytical and numerical methods, we determine the energy spectrum as a function of the magnetic field strength and impurity charge for screened and unscreened Coulomb potentials. Our results reveal a significant dependence of the energy levels for sample-to-gate distances of less than 50 nm.
ER  -