Anomalous Induced Density of Supercritical Coulomb Impurities in Graphene Under Strong Magnetic Fields

Abstract

The Coulomb impurity problem of graphene, in the absence of a magnetic field, displays discrete scale invariance. Applying a magnetic field introduces a new magnetic length scale $\ell$ and breaks discrete scale invariance. Moreover, a magnetic field is a singular perturbation as it turns complex energies into real energies. Nonetheless, the Coulomb potential must be regularized with a length $R$ at short distances for supercritical impurities. We investigate the structure of the induced density of a filled Landau impurity band in the supercritical regime. The coupling between Landau level states by the impurity potential is nontrivial and can lead to several anomalous effects. First, we find that the peak in the induced density can be located away from the center of the impurity, depending on the characteristics of the Landau impurity bands. Second, the impurity charge is screened, despite the Landau impurity band being filled. Third, anticrossing impurity states lead to additional impurity cyclotron resonances.

References in corpus (23)

• The electronic properties of graphene
• Andreev reflection and Klein tunneling in graphene
• The Coulomb impurity problem in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
• Observing Atomic Collapse Resonances in Artificial Nuclei on Graphene
• Quantum Dots in Strong Magnetic Fields: Stability Criteria for the Maximum Density Droplet
• Realization of a Tunable Artificial Atom at a Supercritically Charged Vacancy in Graphene
• Excitations from Filled Landau Levels in Graphene
• Supercritical Coulomb center and excitonic instability in graphene
• Screening of Coulomb Impurities in Graphene
• Coulomb impurity in graphene
• Dirac electron in a Coulomb Field in 2+1 Dimensions
• Planar Dirac Electron in Coulomb and Magnetic Fields
• Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance
• Coulomb impurity under magnetic field in graphene: a semiclassical approach
• Electronic Structure in Gapped Graphene with Coulomb Potential
• Magnetic field dependence of the atomic collapse state in graphene
• Coulomb impurity problem of graphene in magnetic fields
• Screening of a charged impurity in graphene in a magnetic field
• Electron states in the field of charged impurities in two-dimensional Dirac systems
• Resonant, non-resonant, and anomalous states of Dirac electrons in a parabolic well in the presence of magnetic fields
• Impurity cyclotron resonance of anomalous Dirac electrons in graphene