Two-dimensional transmission through modified Pöschl-Teller potential in bilayer graphene

Abstract

We study two-dimensional transport of quasiparticles in bilayer graphene through a modified P\oschl-Teller potential, a potential with hyperbolic profile. Both scattering by well and tunneling through a barrier are investigated. At normal incidence the oscillating and evanescent wave states are completely decoupled, so that only one mode participates in transmission. At oblique incidence a combined contribution of the two modes leads to reduction or enhancement of transmission probability. In both cases the chirality can forbid transition to oscillating modes existing within the well or barrier region, which results in a cloak effect. In the barrier tunneling it appears at normal incidence. In the scattering by the well, however, it arises at an oblique incidence as a consequence of coupling between the positive- and negative-energy states, which we interpret as a secondary cloak effect. When a gap is present in the barrier tunneling, because of the coupling, the transmission probability at and near normal incident angles is greatly enhanced. We also examine the effect of trigonal warping in the barrier tunneling and find valley-dependent transmissions and broadening of resonant-transmission regions. As a result, the resonance curve of conductance has a thicker width and a lower peak-to-bottom contrast than the case without trigonal warping. We demonstrate these phenomena with numerical simulations and explain the results using the chirality-dependent transition probability and semiclassical argument. The numerical results are also compared with those of the corresponding rectangular potential. We observe that the two models display large quantitative differences in their two-dimensional transport.