Edge states in non-Fermi liquids

TL;DR

This paper develops a method to calculate the scaling dimensions of operators in multi-channel Luttinger liquids, revealing conditions under which edge states are robust against disorder in finite arrays.

Contribution

It introduces a novel algebraic approach to analyze impurity scattering in multi-channel Luttinger liquids and identifies conditions for stable edge states without topological order.

Findings

Edge wires are robust against disorder under certain interactions.

Bulk wires tend to become insulating while edges remain conducting.

Edge states can exist without time-reversal symmetry breaking or spin-orbit interaction.

Abstract

We devise an approach to the calculation of scaling dimensions of generic operators describing scattering within multi-channel Luttinger liquid. The local impurity scattering in an arbitrary configuration of conducting and insulating channels is investigated and the problem is reduced to a single algebraic matrix equation. In particular, the solution to this equation is found for a finite array of chains described by Luttinger liquid models. It is found that for a weak inter-chain hybridisation and intra-channel electron-electron attraction the edge wires are robust against disorder whereas bulk wires, on contrary, become insulating. Thus, the edge state may exist in a finite sliding Luttinger liquid without time-reversal symmetry breaking (quantum Hall systems) or spin-orbit interaction (topological insulators).