Visualization of chiral edge states in a magnetic topological insulator

Topological insulators with ferromagnetic ordering exhibit the quantum anomalous Hall effect, in which a chiral one-dimensional edge state encloses an insulating interior. We provide a real-space visualization of the local conductivity profile in Cr modulation doped (Bi,Sb)2Te3 using microwave impedance microscopy (MIM). Well-defined edge states appear in the quantum anomalous Hall regime, which is robust at magnetic fields exceeding the coercive field. Our images reveal a dramatic change in the edge state pattern and microwave response near the topological phase transition between the Chern number N$=$1 and N$=$0 states. By mapping the non-monotonic evolution of the complex microwave response in magnetic field, we construct a phase diagram of competing topological states and unveil the microscopic nature of dissipation and conductivity in each regime.