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 has in-plane $U(1)$ spin rotation symmetry, the noise $S(\omega)$ is given by the fluctuation-dissipation theorem even in the presence of a voltage bias $V$. The noise is strongly dependent on frequency on a small scale $\tau_{K}^{-1}\ll T$ set by the Korringa relaxation rate of the local moment. Exchange components breaking the symmetry give rise to shot noise in the limit of high bias. The differential noise $dS/dV$, commonly measured in experiments, is dominated by the symmetric component up to potentially large bias and disperses strongly with $\omega$ at low frequencies $\omega\sim\tau_{K}^{-1}$, unlike in the case of conventional elastic scatterer where $dS/dV$ is given by white shot noise.