Current Noise from a Magnetic Moment in a Helical Edge

We calculate the two-terminal current noise generated by a magnetic moment coupled to a helical edge of a two-dimensional topological insulator. When the system is symmetric with respect to in-plane spin rotation, the noise is dominated by the Nyquist component even in the presence of a voltage bias V. The corresponding noise spectrum S(V,omega) is determined by a modified fluctuation-dissipation theorem with the differential conductance G(V,omega) in place of the linear one. The differential noise partial derivative S/partial derivative V, commonly measured in experiments, is strongly dependent on frequency on a small scale tau(-1)(K) << T set by the Korringa relaxation rate of the local moment. This is in stark contrast to the case of conventional mesoscopic conductors where partial derivative S/partial derivative V is frequency independent and defined by the shot noise. In a helical edge, a violation of the spin-rotation symmetry leads to the shot noise, which becomes important only at a high bias. Uncharacteristically for a fermion system, this noise in the backscattered current is super-Poissonian.