Band-Gap tuned oscillatory conductance in bilayer graphene n-p-n junction

Abstract

We study transmission of quasiparticles through a bilayer graphene n-p-n junction when the particle energy lies within the band gap produced by external gate fields. The dispersion relation of eigenspectrum allows two pairs of complex-conjugate wave vectors inside the barrier region, so that two types of common paths, [R. Nandkishore and L. Levitov, Proc. Natl. Acad. Sci. 108, 14021 (2011)] one with decaying amplitude and the other with growing amplitude, contribute to the transmission. Each common path produces interference effect of oscillatory transmissions, with vanishing tunneling probabilities at certain values of the band gap and incident angles. We explain this interference effect by using a semiclassical approximation of path integral approach and show that multiple reflection of forward and backward propagations inside the barrier does not destroy the common-path interference. As a result of the interference, we demonstrate that the conductance through the barrier oscillates as a function of the band gap.