Coulomb Problem for Graphene with Supercritical Impurity

[摘要] The properties of charge carriers in graphene with dopants with charge Z within two-dimensional effective Dirac equation with non-zero gap between upper and lower continuums are analyzed. The closed set of explicit equations determining the spectrum of charge carriers are obtained for the case of the Coulomb potential modified at small distances. The critical values Zcrof the dopant charge at which the energy level with the given quantum numbers crosses the lower continuum boundary are determined. For Z crfor several values of the orbital angular momentum, which may take half-integer values in 2D case, dependence of the position of the energy level as a function of charge Z is obtained. For Z > Zcr, the position 0and width γ of the lowest quasidiscrete state are calculated. For such values of Z screening of the impurity charge and resonance scattering of holes are also considered.

[发布机构] National Research Nuclear University MEPhI, Kashirskoe Shosse 31, Moscow; 115409, Russia^1

[效力级别] 数学

[关键词] Coulomb potential;Coulomb problems;Dirac equations;Explicit equations;Integer values;Orbital angular momentum;Quantum numbers;Resonance scattering