We investigate the stabilization of topological Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases, with a specific emphasis on the intraband FFLO phase, in a one-dimensional Fermi gas subjected to an external magnetic field. This research highlights the crucial role of the interplay between Rashba spin-orbit coupling (RSOC) and Dresselhaus spin-orbit coupling (DSOC). Employing a Fermi-Hubbard model alongside the density matrix renormalization group (DMRG) method, we examine the combined effects of RSOC and DSOC on these exotic superfluid phases, taking into account attractive fermionic interactions. Our principal finding reveals that while RSOC primarily stabilizes conventional zero-momentum pairing, DSOC performs a distinct and crucial role in selectively stabilizing the intraband FFLO phase. This stabilization is achieved by enhancing spin polarization within a single helicity band and suppressing interband coherence, thereby facilitating the formation of finite-momentum FFLO pairs within the same band and resulting in the emergence of a topologically nontrivial superfluid. This targeted control of intraband FFLO pairing paves the way for new strategies in the manipulation of superfluid phases in spin-orbit coupled systems and offers essential insights for experimental realizations in ultracold atomic gases, with implications for topological quantum computing and Majorana fermions.

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• Density matrix renormalization group
• FFLO
• Spin-orbit coupling
• Topological superconductors
• 1-dimensional systems
• Superfluids