Structure factor of interacting one-dimensional helical systems

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 vertical bar mu vertical bar < B, the system then behaves as a nonlinear helical Luttinger liquid, and a mobile-impurity analysis reveals power-law singularities in S(q,.) which depend on the interaction strength as well as on the spin texture of the edge states. For vertical bar mu vertical bar > B, the low-energy excitations are gapped, and we determine S(q, omega) by using an analogy to exciton physics.