Finite-frequency admittance and noise of a helical edge coupled to a magnet

The exchange coupling of the helical edge state of a quantum spin-Hall insulator with an easy-plane magnet has no effect on its DC electrical conductance if the magnet's anisotropy axis is aligned with the spin quantization axis of the helical edge state [Meng et al., Phys. Rev. B 90, 205403 (2014)]. We here calculate the AC conductance $G_V(\omega)$ and the noise power $S_V(\omega)$ in the presence of a DC bias $V$. While both take the universal values $G_V({\omega = 0}) = e^2/h$ and $S_V(\omega = 0) = 4 e^2 k_{\rm B} T/h$ in the zero-frequency limit, $G_V(\omega)$ and $S_V(\omega)$ are quickly suppressed for finite $\omega$, so that low-frequency transport is effectively noiseless.