Carbon systems

Electron states in single-layer graphene containing short-range defects: The potential separable in the momentum representation

S. A. Ktitorov^a, Yu. I. Kuzmin^a, N. E. Firsova<sup>b

a</sup> Ioffe Institute, St. Petersburg
^b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg

Abstract: Electron states in single-layer graphene containing short-range defects are studied. A model potential concentrated on a circle and asymmetric with respect to the band number is treated. The study is carried out for the (2 + 1)-dimensional Dirac equation with a potential separable in the angular momentum representation. The characteristic equation derived in the study for bound and resonance states is compared with the equation derived previously for the same system by another method. The momentum representation used in this study provides a means for satisfactorily regularizing the Hadamard-incorrect problem with a singular potential. The method developed here is applied to regularization of the previously derived formulas for the scattering parameters and conductivity in graphene.

Received: 13.01.2011
Accepted: 16.02.2011

 English version: Semiconductors, 2011, 45:9, 1199–1204

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