Local impurity in multichannel Luttinger liquid

TL;DR

This paper analyzes the stability of phases in multichannel Luttinger liquids with impurities, revealing bistability and phase boundary behaviors, especially in two-channel systems, with implications for topological insulators.

Contribution

Develops a general method to determine critical conductance exponents and phase boundaries in multichannel Luttinger liquids, including systems with different channel types.

Findings

System state depends on scattering strength, leading to bistability.

Method applies to fermion-boson mixtures and topological insulator edges.

Interaction alone does not protect topological insulator states.

Abstract

We investigate the stability of conducting and insulating phases in multichannel Luttinger liquids with respect to embedding a single impurity. We devise a general approach for finding critical exponents of the conductance in the limits of both weak and strong scattering. In contrast to the one-channel Luttinger liquid, the system state in certain parametric regions depends on the scattering strength which results in the emergence of a bistability. Focusing on the two-channel liquid, the method developed here enables us to provide a generic analysis of phase boundaries governed by the most relevant (i.e. not necessarily single-particle) scattering mechanism. The present approach is applicable to channels of different nature as in fermion-boson mixtures, or to identical ones as on the opposite edges of a topological insulator. We show that interaction per se cannot provide protection in particular case of topological insulators realized in narrow Hall bars.