Inhomogeneous Topological Superfluidity in One-Dimensional Spin-Orbit-Coupled Fermi Gases

We theoretically predict an exotic topological superfluid state with spatially modulated pairing gap in one-dimensional spin-orbit-coupled Fermi gases. The emergence of this inhomogeneous topological superfluidity is induced by appealing to the conspiration of a perpendicular Zeeman magnetic field and an equally weighted Rashba and Dresselhaus spin-orbit coupling in one-dimensional optical lattices. Based on the self-consistent Bogoliubov-de Gennes theory, we confirm that this novel topological phase is a unique condensation of Cooper pairs, which goes beyond the conventional phase separation phenomena in the artificial confinements. The properties of the emergent Majorana bound states are investigated in detail by examining the associated $\mathbb{Z}_{2}$ topological number, the eigenenergy spectrum, and the wave functions of the localized Majorana end modes.