There is rapidly growing interest in vertically stacked van der Waals materials for electronic device applications. In such structures the interfaces between different materials will, in general, be misoriented with respect to each other. THz cutoff frequencies have been predicted for such devices. Understanding the effect of the misorientation on the interlayer resistance is required to fully understand the design requirements and performance of proposed vertically stacked devices.

The most well studied and well understood of the van der Waals material are graphite and graphene. The effect of misorientation on the electronic structure of bilayer graphene has been studied extensively both theoretically and experimentally. After a few degrees misorientation, the in-plane dispersion becomes linear, and after about 10 degrees misorientation, the in-plane velocity is the same as that of single-layer graphene. Thus, the two misorineted layers of graphene act as if they are electronically decoupled.

The calculated coherent interlayer resistance as a function of rotation
angle θ is found to vary by 16 orders of magnitude as the misorientation
angle changes from zero to 30 degrees. The values vary from
approximately 10^{15} Ωμm^{2} to 0.1 Ωμm^{2}. The
room-temperature, phonon-mediated inter-layer resistance of misoriented
bilayer graphene shows far less dependence on the misorientation angle.
It changes by less than an order of magnitude as the angle varies from
zero to 30 degrees. is approximately 100 Ωμm^{2} over a range of
intermediate rotation angles. Experimental measurements found
approximately an order of magnitude larger resistance that varied from
750 Ωμm^{2} to 3400 Ωμm^{2} as the angle varied from 5^{o} to
24^{o}.

We determined the coherent, interlayer resistance of a misoriented,
rotated interface between two stacks of AB graphite for a variety of
misorientation angles. The quantum-resistance of the ideal AB stack is
on the order of 1 to 10 mΩμm^{2}. For small rotation angles, the
coherent interlayer resistance exponentially approaches the ideal
quantum resistance at energies away from the charge neutrality point.
Over a range of intermediate angles, the resistance increases
exponentially with cell size for minimum size unit cells. Larger cell
sizes, of similar angles, may not follow this trend. The energy
dependence of the interlayer transmission is described.