Abstract
The interaction of two-dimensional quasiparticles characterized by a linear dispersion E = ±u|p| (graphene) with impurity potentials is studied. It is shown that discrete levels corresponding to localized states are present in a one-dimensional potential well (quantum wire), whereas such states are absent in a two-dimensional well (quantum dot). The cross section for the scattering of electrons (holes) of graphene by an axially symmetric potential well is determined. It is shown that the cross section tends to a constant value in the limit of infinite particle energy. The effective Hamiltonian is derived for a curved quantum wire of graphene.
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References
K. S. Novoselov, A. K. Geim, S. V. Morozov, et al., Science 306, 666 (2004).
Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature 438, 201 (2005).
K. S. Novoselov, A. K. Geim, S. V. Morozov, et al., Nature 438, 197 (2005).
V. V. Cheianov and V. I. Fal’ko, Phys. Rev. B 74, 041403(R) (2006).
V. V. Cheianov and V. I. Fal’ko, Phys. Res. Lett. 97, 226801 (2006).
J. Milton Pereira, Jr., V. Mlinar, F. M. Peeters, and P. Vasilopoulos, Phys. Rev. B 74, 045424 (2006).
J. K. Pachos and M. Stone, cond-mat/0607394 (2006).
L. V. Berlyand and S. Yu. Dobrokhotov, Dokl. Akad. Nauk 296, 80 (1987) [Sov. Phys. Dokl. 32, 714 (1987)].
V. V. Belov, S. Yu. Dobrokhotov, and T. Ya. Tudorovskiy, J. Eng. Math. 55, 179 (2006).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory, 4th ed. (Nauka, Moscow 1989; Butterworth, Oxford, 1991).
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Original Russian Text © T.Ya. Tudorovskiy, A.V. Chaplik, 2006, published in Pis’ma v Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 84, No. 11, pp. 735–739.