Geometry-dependent conductance and noise behavior of a graphene ribbon with a series of randomly spaced potential barriers

We perform an envelope-function based numerical analysis of the effect of a sequence of randomly spaced potential barriers on the conductance and shot noise of an armchair graphene ribbon. The behavior is dominated by Klein tunneling and by resonant tunneling and strongly depends on the geometrical details of the device. Klein tunneling effectively filters the modes that can propagate through the device. For a large number of cascaded barriers, this gives rise to different transport regimes for metallic and semiconducting ribbons, with diverging shot noise behaviors. Resonant tunneling is instead energy selective and has quite a different effect depending on whether the barriers are identical or not. We also explore the effect of tilting the barriers with respect to the ribbon edges, observing a transition toward a diffusive transport regime and a one-third shot noise suppression. We investigate this effect, and we find that it takes place also in more traditional semiconducting materials. The results of our analysis could be instrumental for the fabrication of mode-filtering and energy-filtering graphene-based nanodevices. Moreover, our study highlights the importance of the measurement of shot noise as a probe for the nature of the transport regime.