Dynamic structure factor of one-dimensional Fermi superfluid with spin-orbit coupling

We theoretically calculate the density dynamic structure factor of one-dimensional Fermi superfluid with Raman-type spin-orbit coupling, and analyze its main dynamical character during phase transition between Bardeen-Cooper-Schrieffer topological superfluid. Our theoretical results display four kinds single-particle excitations induced by two-branch spectrum, cross excitation is much easier to see in spin at a small transferred momentum. Also we find new rotonlike collective mode emerges fixed momentum $q\ensuremath{\simeq}2{k}_{F}$, it only appears once system enters state. The occurrence this related switch global minimum spectrum from $k=0$ $k\ensuremath{\simeq}2{k}_{F}$.