Giant spin rotation in the junction between a normal metal and a quantum spin Hall system

We study theoretically the reflection problem in the junction between a normal metal and an insulator characterized by a parameter M, which is a usual insulator for M>0 or a quantum-spin-Hall system for M<0. The spin rotation angle alpha at the reflection is obtained as a function of M and the incident angle theta measured from the normal to the interface. The alpha shows rich structures around the quantum critical point M=0 and theta=0; i.e., alpha can be as large as approximately pi at an incident angle in the quantum spin Hall case M<0 because the helical edge modes resonantly enhance the spin rotation, which can be used to map the energy dispersion of the helical edge modes. As an experimentally relevant system, we also study the spin rotation effect in quantum-spin-Hall-normal-metal-quantum-spin-Hall trilayer junction.