Conduction between graphene layers is suppressed by momentum conservation whenever the layer stacking has a rotation. Here we show that phonon scattering plays a crucial role in facilitating interlayer conduction. The resulting dependence on orientat
ion is radically different than previously expected, and far more favorable for device applications. At low temperatures, we predict diode-like current-voltage characteristics due to a phonon bottleneck. Simple scaling relationships give a good description of the conductance as a function of temperature, doping, rotation angle, and bias voltage, reflecting the dominant role of the interlayer beating phonon mode.
Many calculations require a simple classical model for the interactions between sp^2-bonded carbon atoms, as in graphene or carbon nanotubes. Here we present a new valence force model to describe these interactions. The calculated phonon spectrum of
graphene and the nanotube breathing-mode energy agree well with experimental measurements and with ab initio calculations. The model does not assume an underlying lattice, so it can also be directly applied to distorted structures. The characteristics and limitations of the model are discussed.
