Transport through evanescent waves in ballistic graphene quantum dots

We study the transport through evanescent waves in graphene quantum dots of different geometries. The transmission is suppressed when the leads are attached to edges of the same majority sublattice. Otherwise, the transmission depends exponentially on the distance between leads in rectangular dots and as a power law in circular dots. The transmission through junctions, where the transmitted and reflected currents belong to the opposite valley as the incoming one, depends on details of the lattice structure at distances comparable to the atomic spacing.