Structure factor of interacting one-dimensional helical systems

TL;DR

This paper calculates the dynamical structure factor of weakly interacting helical edge states under a magnetic field, revealing interaction-dependent singularities and gapped excitations depending on the chemical potential relative to the magnetic gap.

Contribution

It provides a detailed analysis of the dynamical structure factor in helical systems with magnetic fields, including nonlinear effects and exciton analogy for gapped states.

Findings

Interaction-dependent power-law singularities in S(q,ω) for |μ| > B

Gapped low-energy excitations for |μ| < B

Use of exciton physics analogy to determine S(q,ω) in gapped regime

Abstract

We calculate the dynamical structure factor S(q, {\omega}) of a weakly interacting helical edge state in the presence of a magnetic field B. The latter opens a gap of width 2B in the single-particle spectrum, which becomes strongly nonlinear near the Dirac point. For chemical potentials |{\mu}| > B, the system then behaves as a nonlinear helical Luttinger liquid, and a mobile-impurity analysis reveals interaction-dependent power-law singularities in S(q,{\omega}). For |{\mu}| < B, the low-energy excitations are gapped, and we determine S(q,{\omega}) by using an analogy to exciton physics.