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

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