Regensburg 2010 – scientific programme

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O: Fachverband Oberflächenphysik

O 43: Graphene I

O 43.4: Talk

Wednesday, March 24, 2010, 11:15–11:30, H31

Electronic bound and scattering states in an integrable graphene quantum dot — •George Pal, Walter Apel, and Ludwig Schweitzer — Physikalisch-Technische Bundesanstalt (PTB), Bundesalee 100, 38116 Braunschweig, Germany

We study theoretically the confinement of electrons in a graphene quantum dot created by an electrostatic gate potential applied to single-layer graphene. In the low-energy limit, the electronic properties of graphene are given by a two-dimensional Dirac-like equation for massless chiral electrons. The graphene quantum dot is described by a radially symmetric confining potential with a sharp boundary and that makes the problem analytically integrable. Also, couplings between the graphene layer and the substrate and atomic scale defects and impurities are taken into account by adding a sub-lattice anisotropy and an inter-valley scattering to the Hamiltonian. These terms open a gap in the energy spectrum and allow for the existence of true bound states, forbidden otherwise due to the Klein tunneling phenomenon in an ideal, clean graphene. Considering a wave function with four components (two valleys times two sub-lattice indices), we discuss the conditions for the existence of bound and scattering states for different regimes of the confinement potential. Furthermore, we calculate the energies of the bound states and the scattering matrix. The influence of disorder in the graphene sheet and in the quantum dot is also discussed.