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Hexagonal boron nitride (hBN) is drawing increasing attention as an insulatorand substrate material to develop next generation graphene-based electronicdevices. In this paper, we investigate the quantum transport inheterostructures consisting of a few atomic layers thick hBN film sandwichedbetween graphene nanoribbon electrodes. We show a gate-controllable verticaltransistor exhibiting strong negative differential resistance (NDR) effect withmultiple resonant peaks, which stay pronounced for various device dimensions.We find two distinct mechanisms that are responsible for NDR, depending on thegate and applied biases, in the same device. The origin of first mechanism is aFabry-P\'e like interference and that of the second mechanism is an in-planewave vector matching when the Dirac points of the electrodes align. The hBNlayers can induce an asymmetry in the current-voltage characteristics which canbe further modulated by an applied bias. We find that the electron-phononscattering introduces the decoherence and therefore suppresses first mechanismwhereas second mechanism remains relatively unaffected. We also show that theNDR features are tunable by varying device dimensions. The NDR feature withmultiple resonant peaks, combined with the ultrafast tunneling speed providesprospect for the graphene-hBN-graphene heterostructure in the high-performanceelectronics.

Negative Differential Resistance in Boron Nitride Graphene Heterostructures: Physical Mechanisms and Size Scaling Analysis