Nanoscale imaging of equilibrium quantum Hall edge currents in graphene

The quantum Hall effect has served as a model system to understand topology in condensed matter physics. Although edge states play an important role in explaining the quantization of the Hall conductance, the actual edge currents have evaded direct measurement. Using a scanning nano SQUID-on-tip, we image the equilibrium currents of individual quantum Hall edge states in monolayer graphene. We reveal that the edge states, which are commonly assumed to carry only a chiral downstream current, in fact, carry a pair of counterpropagating currents, in which the topological downstream current in the incompressible region is counterbalanced by a non-topological upstream current flowing in the adjacent compressible region.