In this study, we propose an alternative route to realizing topological superconductivity (TSC). Our approach targets a new class of correlated noncentrosymmetric materials that host two spin-split Fermi surfaces due to spin-orbital intertwined effects. By investigating the superconducting pairings based on two-orbital Rashba-Hubbard model on a square lattice within a spin-fluctuation-mediated pairing framework, we find that, depending on model parameters, the leading superconducting state belongs to the $A_1\left(S_{\pm }\right)$, $B_2$, or $B_2\left(d_{\pm }\right)$ irreducible representations (IRs) of the $C_{4v}$ point group. Notably, the $A_1\left(S_{\pm }\right)$ state features a sign-changed gap between the two spin-split Fermi surfaces and exhibits two key characteristics: (i) it is a parity-mixed state, with the ratio of even-parity to odd-parity components tunable via the Rashba spin-orbit coupling (RSOC) strength and onsite orbital-dependent potential; (ii) it is a fully gapped TSC, characterized by a $Z_2$ topological invariant. When RSOC is strong, the $B_2\left(d_{\pm }\right)$ state can emerge and exhibits both parity-mixed and nodal TSC features. Further analysis reveals that the fully gapped TSC can be predominated by spin-singlet, despite the presence of the spin-triplet components. This distinguishes our case from single-orbital noncentrosymmetric materials, where TSC arises from $p$-wave or $f$-wave spin-triplet pairing. In those systems, the Fermi level must be tuned near a van Hove singularity to enhance ferromagnetic fluctuations that drive the spin-triplet pairing. These distinctions enhance the experimental feasibility of our model.

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• Spin fluctuations
• Spin-orbit coupling
• Noncentrosymmetric materials
• Topological superconductors
• Bogoliubov-de Gennes equations
• Eliashberg theory
• Lattice models in condensed matter
• Random phase approximation