Coulomb impurity under magnetic field in graphene: a semiclassical approach

Details Coulomb impurity under magnetic field in graphene: a semiclassical approach Coulomb impurity under magnetic field in graphene: a semiclassical approach

2012-01-15

arxiv.org/abs/1201.3100v1

Phys. Rev. B 85, 165423 (2012)

Physics

Condensed Matter

Strongly Correlated Electrons

10 pages, 5 figures

Scientific paper

10.1103/PhysRevB.85.165423

We address the problem of a Coulomb impurity in graphene in the presence of a perpendicular uniform magnetic field. We show that the problem can be solved below the supercritical impurity magnitude within the WKB approximation. Without impurity the semiclassical energies correctly reproduce the Landau level spectrum. For a given Landau level the WKB energy depends on the absolute value of angular momentum in a way which is consistent with the exact diagonalization result. Below the supercritical impurity magnitude, the WKB solution can be expanded as a convergent series in powers of the effective fine structure constant. Relevance of our results to validity of the widely used Landau level projection approximation is discussed.

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