Charge-spin duality in non-equilibrium transport of helical liquids

TL;DR

This paper explores the non-equilibrium transport of charge and spin in helical liquids, revealing a duality relation and how spin information can be inferred from charge measurements in quantum spin Hall insulators.

Contribution

It introduces a duality relation between charge and spin sectors in helical Tomonaga Luttinger liquids and demonstrates how spin information can be accessed via charge measurements.

Findings

Charge-spin duality relation in helical liquids

Generation of pure spin density without charge current

Detection of spin information through charge measurements

Abstract

Non-equilibrium transport properties of charge and spin sector of two edges of a quantum spin Hall insulator are investigated theoretically in a four-terminal configuration. A simple duality relation between charge and spin sector is found for two helical Tomonaga Luttinger liquids (hTTLs) connected to non-interacting electron reservoirs. If the hTLLs on opposite edges are coupled locally or non-locally, the mixing between them yields interesting physics where spin information can be easily detected by a charge measurement and vice versa. Particularly, we show how a pure spin density in the absence of charge current can be generated in a setup that contains two hTLL and one spinful Tomonaga Luttinger liquid in between.