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.Comment: 15 pages, 7 figures, v2 refs adde
