2006/10/25 by A. V. Chaplik, Chaplik, A. V., T. Ya. Tudorovskiy +2
Materials Science · Physics and Astronomy · #Carbon Nanotubes in Composites #FOS: Physical sciences #Graphene research and applications #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena #cond-mat.mes-hall
paper · pdf · doi:10.48550/arxiv.cond-mat/0610705
2 figures. The paper was sent to JETP Letters. Reasons for replacing previous versions: added references [4-6], corrected typos
openalex publication_date 2006/10/25 · arxiv created 2006/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.