Field-free anomalous junction and superconducting diode effect in spin-split superconductor/topological insulator junctions

We study the transport properties of a diffusive Josephson junction between two spin-split superconductors (SCs) made SC-ferromagnetic insulator bilayers on top three-dimensional topological insulator. derive corresponding Usadel equation describing quasiclassical Green's functions in these systems and first solve analytically weak-proximity case. demonstrate appearance an anomalous phase absence external magnetic field. also explore nonreciprocal electronic transport. Specifically, we calculate diode efficiency $\ensuremath{\eta}$ by solving equation. obtain sizable effect even at zero applied discuss how depends different parameters find nonmonotonic behavior with temperature.