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31.An electron scattered by hBN reciprocal lattice vector, , while tunnelling between BZ corners and on the BLG/MLG (labelled according to Fig. 1), has its valley momentum shifted by .27 The initial/final state energies in this process are and will therefore be Pauli blocked, for all achievable levels of electrostatic doping, unless . This condition can only be satisfied with if the hBN layer is crystallographically well aligned with the two graphene layers, and the resulting additional tunnelling process can be included into Eq. (5), by replacing throughout, n → m in GML, and .

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We investigate the current-voltage characteristics of a field-effect tunnelling transistor comprised of both monolayer and bilayer graphene with well-aligned crystallographic axes, separated by three layers of hexagonal boron nitride. Using a self-consistent description of the device's electrostatic configuration, we relate the current to three distinct tunable voltages across the system and hence produce a two-dimensional map of the I-V characteristics in the low energy regime. We show that the use of gates on either side of the heterostructure offers a fine degree of control over the device's rich array of characteristics, as does varying the twist between the grapheneelectrodes.


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