Aharonov-Bohm effect and broken valley degeneracy in graphene rings

P. Recher,1,2 B. Trauzettel,3,4 A. Rycerz,5 Ya. M. Blanter,2 C. W. J. Beenakker,1 and A. F. Morpurgo2 1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands 2Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands 3Department of Physics and Astronomy, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland 4Institute for Theoretical Physics and Astrophysics, University of Würzburg, D-97074 Würzburg, Germany 5Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland Received 14 June 2007; revised manuscript received 27 September 2007; published 5 December 2007