Fractional charge and quantized current in the quantum spin Hall state

Soon after the theoretical proposal of the intrinsic spin Hall effect in doped semiconductors, the concept of a time-reversal invariant spin Hall insulator was introduced. In the extreme quantum limit, a quantum spin Hall (QSH) insulator state has been proposed for various systems. Recently, the QSH effect has been theoretically proposed and experimentally observed in HgTe quantum wells. One central question, however, remains unansweredwhat is the direct experimental manifestation of this topologically non-trivial state of matter? In the case of the quantum Hall effect, it is the quantization of the Hall conductance and the fractional charge of quasiparticles, which are results of non-trivial topological structure. Here, we predict that for the QSH state a magnetic domain wall induces a localized state with half the charge of an electron. We also show that a rotating magnetic field can induce a quantized d.c. electric current, and vice versa. Both of these physical phenomena are expected to be direct and experimentally observable consequences of the non-trivial topology of the QSHstate.