Noise in the helical edge channel anisotropically coupled to a local spin

TL;DR

This paper investigates the frequency-dependent shot noise in topological insulator edge states coupled to a magnetic impurity, revealing how anisotropy and spin interactions influence noise characteristics across different regimes.

Contribution

It provides a comprehensive analysis of shot noise behavior considering various anisotropic spin couplings in topological insulator edge states, highlighting new effects of non-spin-conserving scattering.

Findings

At zero anisotropy, noise is thermal at low frequencies and Poissonian at high frequencies.

Spin-flip interactions with conserved electron spins lead to frequency-independent noise at high voltages.

Non-spin-conserving scattering causes frequency-dependent noise with a ratio to backscattering current exceeding 1 at low frequencies.

Abstract

We calculate the frequency-dependent shot noise in the edge states of a two-dimensional topological insulator coupled to a magnetic impurity with spin $S=1/2$ of arbitrary anisotropy. If the anisotropy is absent, the noise is purely thermal at low frequencies, but tends to the Poissonian noise of the full current $I$ at high frequencies. If the interaction only flips the impurity spin but conserves those of electrons, the noise at high voltages $eV\gg T$ is frequency-independent. Both the noise and the backscattering current $I_{bs}$ saturate at voltage-independent values. Finally, if the Hamiltonian contains all types of non-spin-conserving scattering, the noise at high voltages becomes frequency-dependent again. At low frequencies, its ratio to $2eI_{bs}$ is larger than 1 and may reach 2 in the limit $I_{bs}\to 0$. At high frequencies it tends to 1.