Tunable zero-energy transmission resonances in shifted graphene bilayer

Laboratoire de Physique des Mat´eriaux, Facult´e des Sciences de Bizerte,Universit´e de Carthage, Jarzouna, 7021 Bizerte, Tunisie.(Dated: December 16, 2013)A graphene bilayer is known to perfectly reflect normally incident electrons due to their chiral-ity. This is similar to Klein tunneling, which, in a monolayer, is instead responsible for perfecttransmission at normal incidence. Stacking defaults turn each parabolic band crossing of a bilayerinto pairs of Dirac cones. Here we show that, surprisingly, a stacking default (or shift) in a bilayercan result in perfect transmission at normal incidence as a result of Fabry-P´erot type resonancesat zero-energy. These constructive interferences only happen for a specific orientation of the Diraccones with respect to the incident electron and for quantized values of their separation in reciprocalspace. Our results provide a way to control transmission resonances in undoped graphene bilayerstructure by adjusting the layer stacking.I. INTRODUCTION