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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. This inhomogeneous topological superfluidity is induced by applying simultaneously 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 manifests the interplay between the inhomogeneity of superfluid and its nontrivial topological structure. The properties of the emergent Majorana bound states are investigated in detail by examining the associated $\mathbb{Z}_{2}$ topological number, the eigenenergy and density of states spectra, as well as the wave functions of the localized Majorana end modes. Experimental feasibility of observing this new topological state of matter is also discussed.