Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields

TL;DR

This paper theoretically investigates how Rashba spin-orbit coupling and electron-electron interactions influence the formation of helical gaps in nanowires, revealing interaction-induced gaps without magnetic fields and proposing experimental distinctions.

Contribution

It demonstrates that interactions can induce a helical gap in nanowires without magnetic fields and provides a comprehensive analysis of dynamic response functions using advanced theoretical methods.

Findings

Interactions can open a helical gap without magnetic field.

Distinct signatures of magnetic-field-induced and interaction-induced gaps.

Theoretical predictions for experimental identification of helical gaps.

Abstract

A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a "helical gap" manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunnelling density of states. In this paper, we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interactions can open a helical gap even without magnetic field. We calculate the dynamic response functions using bosonization, a renormalization group analysis, and the exact form factors of the emerging sine-Gordon model. For special interaction strengths, we verify our results by refermionization. We show how the two types of helical gaps, caused by magnetic fields or interactions, can be distinguished in experiments.