Tunneling Energy and Capacitance of Twist-Controlled Graphene Double Layers Separated by Boron Nitride Barriers

In recent years, two dimensional (2D) materials-based resonant tunneling devices have been constructed using an increasing variety of electrode and barrier combinations. Consequently, it is informative to experimentally establish the tunneling current-voltage characteristics as a function of barrier parameters, and theoretically capture these data within a model with few tunable parameters. To that end, we study dual-gated double monolayer graphene heterostructures, consisting of two twist aligned graphene electrodes separated by hexagonal boron nitride (hBN) tunnel barriers of different thicknesses. Because the two graphene layers’ crystal axes are aligned throughout fabrication, we observe energy and momentum conserving resonant tunneling characterized by gate-tunable negative differential resistance. Data from a large set of devices show similar resonant tunneling characteristics that can be captured by a simple framework with two barrier-dependent parameters: interlayer hopping energy (t) and interlayer capacitance (C_Int). We find that interlayer hopping energy decreases by three orders of magnitude as the hBN tunnel barrier increases from two to seven layers. We compare the interlayer hopping energy and capacitance to previous data reported in literature.