Regensburg 2007 – scientific programme

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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).