Transport phenomena in helical edge states interferometers. A Green's function approach

TL;DR

This paper investigates electron transport and noise in helical edge state interferometers of topological insulators using Green's functions, revealing interference effects and methods to measure spin-flip scattering.

Contribution

It introduces a Green's function approach to analyze interference and spin-flip effects in helical edge state interferometers with single and double quantum point contacts.

Findings

Identification of interference processes analogous to Fabry-Pérot and Mach-Zehnder interferometers.

Proposal of shot-noise measurement as a tool to quantify spin-flip scattering.

Analysis of current and noise behavior under different scattering and gate voltage configurations.

Abstract

We analyze the current and the shot-noise of an electron interferometer made of the helical edge states of a two-dimensional topological insulator within the framework of non-equilibrium Green's functions formalism. We study in detail setups with a single and with two quantum point contacts inducing scattering between the different edge states. We consider processes preserving the spin as well as the effect of spin-flip scattering. In the case of a single quantum point contact, a simple test based on the shot-noise measurement is proposed to quantify the strength of the spin-flip scattering. In the case of two single point contacts with the additional ingredient of gate voltages applied within a finite-size region at the top and bottom edges of the sample, we identify two type of interference processes in the behavior of the currents and the noise. One of such processes is analogous to that taking place in a Fabry-P\'erot interferometer, while the second one corresponds to a configuration similar to a Mach-Zehnder interferometer. In the helical interferometer these two processes compete.