Screening of a charged impurity in graphene in a magnetic field

Abstract

The electron states in the field of a charged impurity in graphene in a magnetic field are studied numerically. It is shown that a charged impurity removes the degeneracy of Landau levels converting them into bandlike structures. As the charge of impurity grows, the repulsion of sublevels of different Landau levels with the same value of orbital momentum takes place leading to the redistribution of the wave function profiles of these sublevels near the impurity. By studying the polarization effects, it is shown in agreement with the recent experiments that the effective charge of impurity can be very effectively tuned by chemical potential. If the chemical potential is situated inside a Landau level, then the charge of impurity is strongly diminished. In addition, the polarization function in this case has a peak at zero momentum, which leads to the sign-changing oscillations of the screened potential as a function of distance. If the chemical potential lies between the Landau levels, then the screened potential does not change sign, the screening is minimal, and the charged impurity can strongly affect the electron spectrum.

11 pages, 7 figures; final version published in PRB

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• Magnetic field dependence of the atomic collapse state in graphene
• Electron states in the field of charged impurities in two-dimensional Dirac systems
• Characterization and manipulation of intervalley scattering induced by an individual monovacancy in graphene
• Coulomb center instability in bilayer graphene
• Magnetizations and de Haas-van Alphen oscillations in massive Dirac fermions
• Comment on "Impurity spectra of graphene under electric and magnetic fields"
• Tunable circular dipolelike system in graphene: Mixed electron-hole states
• Atomic collapse of high-order singular potentials in graphene
• Anomalous Induced Density of Supercritical Coulomb Impurities in Graphene Under Strong Magnetic Fields