Topological charge pumping effect by the magnetization dynamics on the Surface of Three-Dimensional Topological Insulators

We discuss a current dynamics on the surface of a 3-dimensional topological insulator induced by magnetization precession of a ferromagnet attached. It is found that the magnetization dynamics generates a direct charge current when the precession axis is within the surface plane. This rectification effect is due to a quantum anomaly and is topologically protected. The robustness of the rectification effect against first-varying exchange field and impurities is confirmed by explicit calculation.