Spatially inhomogeneous states of charge carrier in graphene

Details Spatially inhomogeneous states of charge carrier in graphene Spatially inhomogeneous states of charge carrier in graphene

2006-10-25

arxiv.org/abs/cond-mat/0610705v4

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

2 figures. The paper was sent to JETP Letters. Reasons for replacing previous versions: added references [4-6], corrected typo

Scientific paper

We study an interaction of 2D quasiparticles with linear dispersion (graphene) with impurity potentials. It is shown that in 1D potential well (quantum wire) there are discrete levels, corresponding to localized states, whereas in 2D well (quantum dot) there are no such states. Scattering cross-section of electrons (holes) of graphene by an axially symmetric potential well is found and it is shown that for infinetily large energy of incoming particles the cross-section tends to a constant. The effective Hamiltonian for a curved quantum wire of graphene is derived and it is shown that the corresponding geometric potential cannot form 1D bound states.

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