Quantum Interference at the Twist Boundary in Graphene

We explore the consequences of a rotation between graphene layers for the electronic spectrum. We derive the commensuration condition in real space and show that the interlayer electronic coupling is governed by an equivalent commensuration in reciprocal space. The larger the commensuration cell, the weaker the interlayer coupling, with exact decoupling for incommensurate rotations and in the theta-->0 limit. Furthermore, from first-principles calculations we determine that even for the smallest possible commensuration cell the decoupling is effectively perfect, and thus graphene layers will be seen to decouple for all rotation angles.