Abstract
Analytical solutions to the Coulomb impurity problem of graphene in the absence of a magnetic field show that when the dimensionless strength of the Coulomb potential g reaches a critical value the solutions become supercritical with imaginary eigenenergies. Application of a magnetic field is a singular perturbation, and no analytical solutions are known except at a denumerably infinite set of magnetic fields. We find solutions to this problem by numerical diagonalization of the large Hamiltonian matrices. Solutions are qualitatively different from those of zero magnetic field. All energies are discrete and no complex energies are allowed. We have computed the finite-size scaling function of the probability density containing an s-wave component of the Dirac wavefunctions. This function depends on the coupling constant, regularization parameter, and the gap. In the limit of vanishing regularization parameter our findings are consistent with the expected values of the exponent ν which determines the asymptotic behavior of the wavefunction near r = 0.
Original language | English |
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Pages (from-to) | 21-31 |
Number of pages | 11 |
Journal | Annals of Physics |
Volume | 347 |
DOIs | |
Publication status | Published - 2014 Aug |
Bibliographical note
Funding Information:This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (MSIP) ( NRF-2012R1A1A2001554 ). In addition this research was supported by a Korea University Grant.
Keywords
- Coulomb impurity problem
- Graphene
- Supercritical
ASJC Scopus subject areas
- General Physics and Astronomy