Although the recently predicted topological magnetoelectric effect¹ and the response to an electric charge that mimics an induced mirror magnetic monopole² 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-tip³, 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 models². 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 currents⁴, 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.

尽管最近预测的拓扑磁电效应¹和对模拟感应镜像磁单极子^2的电荷的响应是具有颠倒的时间反转对称性的事物的拓扑状态的基本属性，但到目前为止，还没有在实验中直接观察到它们。使用尖端³的SQUID ，同时充当可调扫描电荷和超灵敏纳米磁力计，我们感应并直接成像在石墨烯量子霍尔电子系统中产生磁单极响应的微观电流。我们发现由拓扑和非拓扑平衡电流共存控制的丰富而复杂的非线性行为，这不是单极子模型所捕获的²。此外，通过对单个量子霍尔边缘状态的平衡电流进行成像，我们发现通常假定仅携带手性下游电流的边缘状态实际上携带一对反向传播电流⁴，其中拓扑下游电流为不可压缩区域由在相邻可压缩区域中流动的非拓扑上游电流平衡。反向传播的平衡态轨道电流的复杂模式提供了对量子霍尔系统中拓扑和非拓扑电荷与能量流的微观起源的深刻见解。