We propose a theoretical framework for the realization of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing in a helical Shiba chain subjected to an out-of-plane Zeeman field, analyzed through a self-consistent Bogoliubov–de Gennes mean-field formalism approach. A chain of magnetic adatoms with helical spin texture deposited on the surface of a common $s$-wave superconductor has emerged as a pivotal platform for realizing topological Majorana zero modes (MZMs). Our study reveals the crucial role of finite momentum pairing of Cooper pairs in the form of a FFLO state which also supports topological MZMs at the ends of the chain. Interestingly, we demonstrate that FFLO pairing facilitates nonreciprocal charge transport, giving rise to a superconducting diode effect in our system where both time-reversal and inversion symmetries are broken. Such a diode effect stems directly from the presence of finite Cooper pair momentum of the FFLO ground state. Our comprehensive analysis highlights the intricate interplay between the richness of the helical Shiba chain, out-of-plane Zeeman field, and FFLO pairing in the emergence of MZMs and driving the superconducting diode effect. These findings offer valuable insights into the design and realization of topological superconducting devices with diode-like properties, potentially advancing technological applications in quantum computing and superconducting electronics.

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• FFLO
• Majorana fermions
• Topological superconductors
• 1-dimensional spin chains
• Diodes
• Superconducting devices
• Exact diagonalization
• Mean field theory