nanoelectronics - Institut d'Études Scientifiques de Cargèse (IESC)

Friday
Electron focusing in grapheme
Csaba Péterfalvi 1,2 , László Oroszlány 1 , József Cserti 1 , Colin Lambert 2
1 Department of Physics of Complex Systems, Eötvös University, Budapest, H-1117,
Hungary
2 Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
We propose an implementation of a valley selective electronic Veselago lens, as a planar
potential step in bilayer graphene. We demonstrate that low energy electrons radiating from
a point source and being scattered by an appropriately oriented potential step can be
focused again coherently within the same band. The phenomenon is due to the negative
refraction index which is a consequence of the anisotropy in the dispersion relation caused
by the trigonal warping effect. We also consider an effective Hamiltonian in which the
electron-electron interaction [1], as well as external mechanical strain [2] is taken into
account, and we show how this affects the focusing phenomenon. Recent studies on the
electron-phonon interaction in bilayer graphene [3] suggest that the electrons' free path can
be long enough even on room temperatures to enable the focusing.
[1] Y. Lemonik, I. L. Aleiner, C. Toke, and V. I. Fal’ko, Spontaneous symmetry breaking and
Lifshitz transition in bilayer graphene, Phys. Rev. B 82, 201408 (2010)
[2] M. Mucha-Kruczyński, I. L. Aleiner and V. I. Fal’ko, Strained bilayer graphene: Band
structure topology and Landau level spectrum, Phys. Rev. B 84, 041404 (2011)
[3] K. M. Borysenko, J. T. Mullen, X. Li, Y. G. Semenov et al, Electron-phonon interactions in
bilayer graphene, Phys. Rev. B 83, 161402 (2011)
__________________________________________________________________________
Theory of scanning gate microscopy
C. Gorini 1 , R. A. Jalabert 1 , W. Szewc 1 , S. Tomsovic 2 and D. Weinmann 1
1 Institut de Physique et Chimie des Matérieux de Strasbourg, UMR 7504, CNRS-UdS, 23 rue
du Loess, BP 43, 67034 Strasbourg Cedex 2, France
2 Department of Physics and Astronomy, PO Box 642814, Washington State University,
Pullman, WA 99164-2814, USA
The conductance change due to a local perturbation in a phase-coherent nanostructure is
calculated [1]. The general expressions to first and second order in the perturbation are
applied to the scanning gate microscopy of a two-dimensional electron gas containing a
quantum point contact. The relation between the conductance change and the local current
density is discussed relying on an extension of the Szafer-Stone model for a constriction [2].
[1] R. A. Jalabert, W. Szewc, S. Tomsovic and D. Weinmann, What is measured in the
scanning gate microscopy of a quantum point contact? Phys. Rev. Lett. 105 166802 (2010)
[2] A. Szafer and A. D. Stone, Theory of Quantum Conduction through a Constriction Phys.
Rev. Lett. 62 300 (1989)