Current noise from a magnetic moment in a helical edge

TL;DR

This paper analyzes the current noise generated by a magnetic moment on a helical edge of a topological insulator, revealing unique frequency-dependent noise characteristics and the impact of spin-rotation symmetry violations.

Contribution

It provides a theoretical calculation of current noise in a helical edge system, highlighting the role of symmetry and the Korringa relaxation rate in noise behavior.

Findings

Noise dominated by Nyquist component under symmetry

Frequency dependence of differential noise related to Korringa rate

Shot noise appears when spin-rotation symmetry is broken

Abstract

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.