Field-free Superconducting Diode Effect and Topological Fulde-Ferrell-Larkin-Ovchinnikov Superconductivity in Altermagnetic Shiba Chains

Abstract: The superconducting diode effect (SDE), characterized by a directional asymmetry in the critical supercurrents, typically requires external magnetic fields to break time-reversal symmetry -- posing challenges for scalability and device integration. Here, we demonstrate a field-free realization of the SDE in a helical Shiba chain proximitized by a d-wave altermagnet. Using a self-consistent Bogoliubov-de Gennes approach, we uncover a topological Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state that hosts tunable Majorana zero modes at the chain ends. This state is stabilized by the interplay between the exchange coupling of magnetic adatoms and the induced altermagnetic spin splitting. Crucially, the same FFLO phase supports strong nonreciprocal supercurrents, achieving diode efficiencies exceeding 45% without applied magnetic fields. The d-wave altermagnet plays a dual role: it intrinsically breaks time-reversal symmetry, enabling topological superconductivity, and introduces inversion symmetry breaking via momentum-dependent spin-splitting, driving the field-free SDE in a junction-free setting. The supercurrent-controlled finite Cooper pair momentum of the FFLO state modulates both the topological gap and the diode response. Our results establish the Shiba chain-altermagnet heterostructure as a promising platform for realizing topological superconducting devices with efficient, intrinsic superconducting diode functionality -- offering a scalable pathway towards dissipationless quantum technologies.