When we drive a current through a quantum anomalous Hall insulator, where does it flow? A view informed by measuring a spatial variation of potential in the presence of weak dissipation

Ideally, quantum anomalous Hall systems should display zero longitudinal resistance. Yet in experimental practice elevated temperature can make the longitudinal resistance finite, indicating dissipative flow of electrons. Here, we show that this can give insights into how and where the current flows, even when the dissipation is very weak ($ ho_{ m xx}sim 10^{-2} e^2/h$.) We find that the measured potentials at multiple locations within a (Cr,Bi,Sb)$_2$Te$_3$ Hall bar are well-described by solution of Laplace's equation, assuming spatially-uniform conductivity. This suggests that non-equilibrium current flows through the two-dimensional bulk. Extrapolation suggests that at even lower temperatures current may still flow primarily through the two-dimensional bulk rather than, as had been assumed, through edge modes. An argument for bulk current flow previously applied to quantum Hall systems supports this picture.