Fractional Charge and Quantized Current in the Quantum Spin Hall State

A profound manifestation of topologically non-trivial states of matter is the occurrence of fractionally charged elementary excitations. The quantum spin Hall insulator state is a fundamentally novel quantum state of matter that exists at zero external magnetic field. In this work, we show that a magnetic domain wall at the edge of the quantum spin Hall insulator carries one half of the unit of electron charge, and we propose an experiment to directly measure this fractional charge on an individual basis. We also show that as an additional consequence, a rotating magnetic field can induce a quantized dc electric current, and vice versa.