• 文献标题:   Coulomb Problem for Z > Z(cr) in Doped Graphene
  • 文献类型:   Article
  • 作  者:   KULESHOV VM, MUR VD, FEDOTOV AM, LOZOVIK YE
  • 作者关键词:  
  • 出版物名称:   JOURNAL OF EXPERIMENTAL THEORETICAL PHYSICS
  • ISSN:   1063-7761 EI 1090-6509
  • 通讯作者地址:   Natl Res Nucl Univ MEPhI
  • 被引频次:   0
  • DOI:   10.1134/S1063776117120160
  • 出版年:   2017

▎ 摘  要

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, +/- 1, +/- 2, aEuro broken vertical bar. For J = 0, +/- 1/2, +/- 1, critical values of the effective charge Z (cr)(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z (cr) (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z > Z (cr) (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions epsilon(0) and widths gamma of quasistationary states as a function of supercriticality. The values of epsilon(0)* and width gamma* are pointed out for which quasidiscrete levels may show up as Breit-Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z (cr). In this single-particle approximation, there is no spontaneous creation of electron-hole pairs, and the impurity charge cannot be screened by this mechanism.