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Spectra of Electronic Excitations in Graphene Near Coulomb Impurities

  • ELECTRONIC PROPERTIES OF SOLID
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Abstract

We study the problem of the electron excitation spectrum in the presence of point-like and regularized Coulomb impurities in gapped graphene. To this end, we use the Dirac model and in the point-like case theory of self-adjoint extensions of symmetric operators. In the point-like case, we construct a family of self-adjoint Hamiltonians describing the excitations for any charge of an impurity. Spectra and (generalized) eigenfunctions for all such Hamiltonians are found. Then, we consider the spectral problem in the case of a regularized Coulomb potential of impurities for a special regularization. We study exact equations for charges of impurities that may generate bound states with energy that coincides with the upper boundary of the negative branch of the continuous spectrum (supercritical charges) and calculate these charges.

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Notes

  1. Note also that the standard QED vacuum in (3+1) dimensions becomes unstable due to the Coulomb attraction between electron and positron above a critical value of the fine-structure constant [2, 3], αcr = π/8 or, with its genuine value of α = 1/137, but if an external magnetic field above 1042 G is imposed [3].

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ACKNOWLEDGMENTS

The work is supported by Russian Science Foundation (Grant no. 19-12-00042).

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Authors and Affiliations

  1. Department of Physics, Tomsk State University, 634050, Tomsk, Russia

    A. I. Breev & D. M. Gitman

  2. Institute of Physics, University of Sao Paulo, 70297-400, Sao Paulo, Brazil

    R. Ferreira & D. M. Gitman

  3. Lebedev Physical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    D. M. Gitman & B. L. Voronov

Authors
  1. A. I. Breev
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  2. R. Ferreira
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  3. D. M. Gitman
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  4. B. L. Voronov
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Correspondence to A. I. Breev, R. Ferreira, D. M. Gitman or B. L. Voronov.

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Breev, A.I., Ferreira, R., Gitman, D.M. et al. Spectra of Electronic Excitations in Graphene Near Coulomb Impurities. J. Exp. Theor. Phys. 130, 711–736 (2020). https://doi.org/10.1134/S1063776120030127

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  • DOI: https://doi.org/10.1134/S1063776120030127

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