  We present the results of an experimental study of the interaction of
quantized Landau level (LL) edge-states at the physical edge of graphene by
using a graphene pn junction device with a ring-shaped geometry for the
channel. The unique device geometry allows the interactions between edge-states
to be probed at both electrostatic edges defined by pn junctions and at the
graphene physical edge. Measurements show that while the lowest LL edge-state
is decoupled from the other LLs along the electrostatic junction, all the
edge-states strongly equilibrate at the graphene physical edge despite the
relatively short distance that they travel along the edge in our device. These
findings are fundamental for the engineering of future high-performance
graphene field-effect transistors based upon electron optics.
