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 $\partial S/ \partial V$, commonly measured in experiments, is strongly dependent on frequency on a small scale $\tau_{K}^{-1}\ll T$ set by the Korringa relaxation rate of the local moment. This is in stark contrast with the case of conventional mesoscopic conductors where $\partial S/ \partial V$ 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.