Tunable zero-energy transmission resonances in shifted graphene bilayer

A graphene bilayer is known to perfectly reflect normally incident electrons due to their chirality. This is similar to Klein tunneling, which, in a monolayer, is instead responsible for perfect transmission at normal incidence. Stacking defaults turn each parabolic band crossing of a bilayer into pairs of Dirac cones. Here we show that, surprisingly, a stacking default (or shift) in a bilayer can result in perfect transmission at normal incidence as a result of Fabry-Perot type resonances at zero energy. These constructive interferences only happen for a specific orientation of the Dirac cones with respect to the incident electron and for quantized values of their separation in reciprocal space. Our results provide a way to control transmission resonances in an undoped graphene bilayer structure by adjusting the layer stacking.