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 $G_V(\omega =0)=e^2\mathrm{/}h$ and $S_V(\omega =0)=4e^2{k}_{\mathrm{B}}T\mathrm{/}h$ 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.