Sub- to Super-Poissonian crossover of current noise in helical edge states coupled to a spin impurity in a magnetic field

TL;DR

This paper investigates how a magnetic field influences current noise in helical edge states coupled to a spin impurity, revealing a transition from antibunching to bunching behavior due to the edge state's helicity.

Contribution

It introduces a detailed analysis of backscattering current noise in helical edge states with a spin impurity, highlighting the transition from sub-Poissonian to super-Poissonian noise.

Findings

Transition from sub-Poissonian to super-Poissonian noise with bias voltage and magnetic field angle.

Quantitative interpretation of Fano factor in terms of electron bunching and antibunching.

Effect of electron-electron interactions analyzed via Tomonaga-Luttinger liquid theory.

Abstract

Edge states of two-dimensional topological insulators are helical and single-particle backscattering is prohibited by time-reversal symmetry. In this work, we show that an isotropic exchange coupling of helical edge states (HES) to a spin 1/2 impurity subjected to a magnetic field results in characteristic backscattering current noise (BCN) as a function of bias voltage and tilt angle between the direction of the magnetic field and the quantization axis of the HES. In particular, we find transitions from sub-Poissonian (antibunching) to super-Poissonian (bunching) behavior as a direct consequence of the helicity of the edge state electrons. We use the method of full counting statistics within a master equation approach treating the exchange coupling between the spin-1/2 impurity and the HES perturbatively. We express the BCN via coincidence correlation functions of scattering processes between the HES which gives a precise interpretation of the Fano factor in terms of bunching and antibunching behavior of electron jump events. We also investigate the effect of electron-electron interactions in the HES in terms of the Tomonaga-Luttinger liquid theory.