Current Correlations in Quantum Spin Hall Insulators

TL;DR

This paper analyzes current correlations in quantum spin Hall insulators with interacting helical edge states, revealing how different transport channels influence noise and cross-correlations, aiding experimental understanding.

Contribution

It provides an exact treatment of electron-electron interactions in helical Luttinger liquids and derives the cumulant generating function for inter-edge current in a four-terminal setup.

Findings

Different transport channels produce distinct noise signatures.

Electron-electron interactions significantly affect current correlations.

Experimental signatures can reveal the interplay between interactions and helical edge states.

Abstract

We consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the electron-electron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the inter-edge current. We show that different possible transport channels give rise to different signatures in the current noise and current cross-correlations, which could be exploited in experiments to elucidate the interplay between electron-electron interactions and the helical nature of the edge states.