Abstract
The properties of charge carriers in doped graphene are considered. The closed set of explicit equations determining the spectrum and wavefunctions of charge carriers for total angular momentum J = M + 1/2 = 0, ±1/2, ±1… is obtained for the case of the Coulomb potential modified at small distances. The critical values Zcr of the dopant charge at which the energy level with the given quantum numbers crosses the lower continuum boundary are determined. For Z < Zcr for several values of the orbital angular momentum dependence of the position of the energy level as a function of charge Z is obtained. For Z > Zcr, the position ε0 and width γ of the lowest quasidiscrete state, which may manifest itself as a resonance in hole-dopant scattering, are calculated. It’s shown that there is no electron-hole pairs creation because of unitarity of the partial scattering matrix.
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