Anomalous Edge Plasmon in magnetically doped topological insulator

Magnetically doped topological insulators (MTIs) with ferromagnetic dopants such as chromium support a Quantum Anomalous Hall Effect state. We show that the quantum anomalous effect necessarily leads to a chiral one dimensional edge plasmon collective mode with approximately linear dispersion, which we refer to as anomalous edge plasmons (AEPs). AEPs are closely related to the so-called Edge Magneto Plasmon (EMP) excitations of two-dimensional electron gases on quantum Hall plateaus in a strong magnetic field, and typically have frequencies in Microwave or Radio frequency ranges, depending on samples size. Recently, researchers in Stanford University used Microwave Impedance Microscopy (MIM) to image quantum anomalous Hall states, and identified response that is localized near Hall bar edges. We interpret these observations in terms of the properties of AEPs, addressing in particular the dependence of the degree of edge localization on the MIM imaging frequency. We also address the influence of magnetic domains on the MIM signal, and discuss the drastic difference between the MIM signal of the quantum anomalous Hall state and the axion insulator state which forms when the magnetization has opposite signs near the top and bottom surfaces of MTI thin films.