Nature Physics | 2019
Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene
Abstract
Although the recently predicted topological magnetoelectric effect 1 and the response to an electric charge that mimics an induced mirror magnetic monopole 2 are fundamental attributes of topological states of matter with broken time-reversal symmetry, so far they have not been directly observed in experiments. Using a SQUID-on-tip 3 , acting simultaneously as a tunable scanning electric charge and as an ultrasensitive nanoscale magnetometer, we induce and directly image the microscopic currents generating the magnetic monopole response in a graphene quantum Hall electron system. We find a rich and complex nonlinear behaviour, governed by the coexistence of topological and non-topological equilibrium currents, that is not captured by the monopole models 2 . Furthermore, by imaging the equilibrium currents of individual quantum Hall edge states, 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 4 , in which the topological downstream current in the incompressible region is counterbalanced by a non-topological upstream current flowing in the adjacent compressible region. The intricate patterns of the counterpropagating equilibrium-state orbital currents provide insights into the microscopic origins of the topological and non-topological charge and energy flow in quantum Hall systems. The microscopic quantum Hall edge currents and the equilibrium currents that generate the mirror magnetic monopoles in time-reversal-symmetry-broken topological matter are directly imaged in the quantum Hall state in graphene by using a SQUID-on-tip.