Interaction-enhanced magnetically ordered insulating state at the edge of a two-dimensional topological insulator

TL;DR

This paper develops a theory showing how electron interactions enhance magnetic ordering at the edge of a 2D topological insulator, with a measurable gap scaling that reveals quantum criticality.

Contribution

It introduces a model linking electron interactions to magnetic gap enhancement and predicts a specific scaling law for the gap in helical liquids.

Findings

The magnetic gap scales as B^{1/(2-K)} with magnetic field B.

The conductance exhibits activation behavior related to the gap.

The results enable experimental extraction of the Luttinger parameter K.

Abstract

We develop a theory of the correlated magnetically ordered insulating state at the edge of a two-dimensional topological insulator. We demonstrate that the gapped spin-polarized state, induced by the application of the magnetic field $B$, is naturally facilitated by electron interactions, which drive the critical easy-plane ferromagnetic correlations in the helical liquid. As the key manifestation, the gap $\De$ in the spectrum of collective excitations, which carry both spin and charge, is enhanced and exhibits a scaling dependence $\De \propto B^{1/(2-K)}$, controlled by the Luttinger liquid parameter $K$. This scaling dependence could be probed through the activation behavior $G \sim (e^2/h) \exp(- \De/T)$ of the longitudinal conductance of a Hall-bar device at lower temperatures, providing a straightforward way to extract the parameter $K$ experimentally. Our findings thus suggest that the signatures of the interaction-driven quantum criticality of the helical liquid could be revealed already in a standard Hall-bar measurement.