Spin polarised scanning tunneling probe for helical Luttinger liquids

TL;DR

This paper introduces a three-terminal spin-polarized STM setup to probe the helical edge states in quantum spin Hall systems, revealing spin fractionalization and a spin current amplification effect.

Contribution

It proposes a novel three-terminal spin-polarized STM method to detect spin fractionalization in helical Luttinger liquids, highlighting the dependence of conductance on magnetization angle.

Findings

Conductance depends on the angle between tip magnetization and electron spin orientation.

Chiral injection leads to fractionalization of both spin and charge.

Spin fractionalization induces a spin current amplification effect.

Abstract

We propose a three terminal spin polarized stm setup for probing the helical nature of the Luttinger liquid edge state that appears in the quantum spin Hall system. We show that the three-terminal tunneling conductance strongly depends on the angle ($\theta$) between the magnetization direction of the tip and the local orientation of the electron spin on the edge while the two terminal conductance is independent of this angle. We demonstrate that chiral injection of an electron into the helical Luttinger liquid (which occurs when $\theta$ is zero or $\pi$) is associated with fractionalization of the spin of the injected electron in addition to the fractionalization of its charge. We also point out a spin current amplification effect induced by the spin fractionalization.