  The recently predicted topological magnetoelectric effect and the response to
an electric charge that mimics an induced mirror magnetic monopole are
fundamental attributes of topological states of matter with broken time
reversal symmetry. Using a SQUID-on-tip, acting simultaneously as a tunable
scanning electric charge and as 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 behavior governed by coexistence of topological and
nontopological equilibrium currents that is not captured by the monopole
models. Furthermore, by utilizing a tuning fork that induces nanoscale
vibrations of the SQUID-on-tip, we directly image the equilibrium currents of
individual quantum Hall edge states for the first time. We reveal that the edge
states that 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 always counterbalanced by
heretofore unobserved nontopological upstream current flowing in the adjacent
compressible region. The intricate patterns of the counterpropagating
equilibrium-state orbital currents provide new insights into the microscopic
origins of the topological and nontopological charge and energy flow in quantum
Hall systems.
