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

TL;DR

This paper investigates the AC conductance and noise characteristics of a helical edge state in a quantum spin-Hall insulator coupled to a magnet, revealing frequency-dependent suppression of conductance and noise.

Contribution

It provides the first calculation of finite-frequency admittance and noise for a helical edge-magnet system, extending understanding beyond DC properties.

Findings

Zero-frequency conductance and noise are universal values.

Finite frequency causes rapid suppression of conductance and noise.

Low-frequency transport becomes effectively noiseless.

Abstract

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.