Transport between twisted graphene layers

Commensurate- incommensurate transitions are ubiquitous in physics and are often accompanied by intriguing phenomena. In few-layer graphene (FLG) systems, commensurability between honeycomb lattices on adjacent layers is regulated by their relative orientation angle theta, which is in turn dependent on sample preparation procedures. Because incommensurability suppresses interlayer hybridization, it is often claimed that graphene layers can be electrically isolated by a relative twist, even though they are vertically separated by a fraction of a nanometer. We present a theory of interlayer transport in FLG systems which reveals a richer picture in which the specific conductance depends sensitively on theta, single-layer Bloch-state lifetime, in-plane magnetic field, and bias voltage. We find that linear and differential conductances are generally large and negative near commensurate values of theta, and small and positive otherwise. We show that accounting for interlayer coupling may be essential for describing transport in FLG despite its physically insignificant effect on the band structure of the system.