Noiseless manipulation of helical edge state transport by a quantum magnet

The current through a helical edge state of a quantum-spin-Hall insulator may be fully transmitted through a magnetically gapped region due to a combination of spin-transfer torque and spin pumping [Meng {\em et al.}, Phys. Rev. B {\bf 90}, 205403 (2014)]. Using a scattering approach, we here argue that in such a system the current is effectively carried by electrons with energies below the magnet-induced gap and well below the Fermi energy. This has striking consequences, such as the absence of shot noise, an exponential suppression of thermal noise, and an obstruction of thermal transport. For two helical edges covered by the same quantum magnet, the device can act as robust noiseless current splitter.