Van der Waals (vdW) heterostructures assembled from graphene and hexagonal boron nitride (h-BN) provide a platform for investigating fundamental physics and also novel electronic properties that could be exploited for devices. Graphene/h-BN heterostructures have higher carrier mobility and better device performance when compared with traditional graphene-based devices on SiO2/Si substrate. Vertical interlayer tunneling in graphene/h-BN/graphene structures also exhibit negative differential resistance (NDR). These electrical properties have attracted considerable attention for energy band engineering and device performance optimization.

Due to the intrinsic vdW forces between the layers, graphene stacked on h-BN tends to be misoriented relative to the h-BN layer. Interlayer electron transport through a graphene / rotated h-BN / graphene heterostructure is strongly affected by the misorientation angle θ of the h-BN with respect to the graphene layers with different physical mechanisms governing the transport in different regimes of angle, Fermi level, and bias. The different mechanisms and their resulting signatures in resistance and current are analyzed using two different models, a tight-binding, nonequilibrium Green's function model and an effective continuum model. The qualitative features resulting from the two different models compare well. In the large-angle regime (θ > 4°), the change in the effective h-BN bandgap seen by an electron at the K point of the graphene causes the resistance to monotonically increase with angle by several orders of magnitude reaching a maximum at θ = 30°. It does not affect the peak-to-valley current ratios in devices that exhibit negative differential resistance. In the small-angle regime (θ < 4°), Umklapp processes open up new conductance channels that manifest themselves as non-monotonic features in a plot of resistance versus Fermi level that can serve as experimental signatures of this effect. For small angles and high bias, the Umklapp processes give rise to two new current peaks on either side of the direct tunneling peak.

Electronic properties of a bilayer graphene/h-BN heterostructure are studied using a continuum model. The simulation results show that the resistance at the secondary Dirac cone as function of vertical electric field exhibits strong electron-hole asymmetry. First principles simulations were used to understand the effect of a rotated h-BN substrate on the electronic properties of trilayer graphene. Finally, tetra-layer graphene's transport properties are studied using a tight-binding model and Boltzmann transport theory. The interband and intraband scattering mechanisms give a good explanation of the experimental results.