The Helical Liquid and the Edge of Quantum Spin Hall Systems

TL;DR

This paper investigates the properties of helical liquids at the edges of quantum spin Hall systems, proving a no-go theorem for certain configurations and exploring interaction effects and impurity responses.

Contribution

It establishes a no-go theorem for odd-component helical liquids in 1D lattices and analyzes interaction-induced gaps and impurity effects in these systems.

Findings

No odd-component helical liquids in purely 1D lattice systems.

Interactions can induce a ground state gap when TR symmetry is broken.

Impurities can lead to relevant backscattering and unique Kondo effects.

Abstract

The edge states of the recently proposed quantum spin Hall systems constitute a new symmetry class of one-dimensional liquids dubbed the ``helical liquid'', where the spin orientation is determined by the direction of electron motion. We prove a no-go theorem which states that a helical liquid with an odd number of components cannot be constructed in a purely 1D lattice system. In a helical liquid with an odd number of components, a uniform gap in the ground state can appear when the time-reversal (TR) symmetry is spontaneously broken by interactions. On the other hand, a correlated two-particle backscattering term by an impurity can become relevant while keeping the TR invariance. The Kondo effect in such a liquid exhibits new features in the structure of the screening cloud.