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HL: Fachverband Halbleiterphysik
HL 49: Graphene
HL 49.2: Talk
Thursday, March 29, 2007, 17:45–18:00, H17
Spatially inhomogeneous states of charge carriers in graphene — Alexander Chaplik1 and •Timur Tudorovskiy2 — 1Institute of Semiconductor Physics, 630090, Novosibirsk, Russia — 2AG QChaos, FB Physik, Universität Marburg, Renthof 5, 35032 Marburg, Germany
Monatomic layers of carbon atoms, forming hexagonal lattice (graphene), are studied very intensively at present [1-2]. A “conical” dispersion law for free quasiparticles E=± u|p| implies crucial distinctions of their dynamical characteristics from the corresponding characteristics of massive particles. We study an interaction of 2D quasiparticles with impurity potentials assuming that it can be described by the effective equation u(σ p)Ψ+v(r)Ψ=EΨ, where σ=(σ1,σ2) are Pauli matrices, p=−iℏ∇ is momentum operator, u is characteristic velocity and v(r) is an impurity potential.
We consider some simple exactly solvable
models of 1D and 2D potential wells from the viewpoint of
possibility to localize quasiparticles.
It is shown, that in quantum wires transversal (1D) localization
is possible, whereas in quantum dots as well as for hydrogen-like donors
or acceptors 2D localization is not possible.
Scattering cross-sections
of electrons (holes) of graphene by an axially symmetric potential
well are obtained. It is shown that in the limit of infinitely large energies of
incoming particles the cross-section tends to a constant.
It is shown that the geometric potential for a curved quantum wire
differs from the case of parabolic
dispersion law, and cannot form 1D bound states.
K. S. Novoselov et al., Science, 306, 666 (2004).
J. Milton Pereira et al., Phys. Rev. B 74, 045424 (2006).