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 made of superconductor-ferromagnetic insulator bilayers (FIS) on top of a 3D topological insulator (TI). We derive the corresponding Usadel equation describing the quasiclassical Green's functions in these systems and first solve the equation analytically in the weak-proximity case. We demonstrate the appearance of an anomalous phase in the absence of an external magnetic field. We also explore non-reciprocal electronic transport. Specifically, we calculate the junction's diode efficiency $\eta$ by solving the Usadel equation. We obtain a sizable diode effect even at zero applied magnetic field. We discuss how the diode efficiency $\eta$ depends on the different parameters and find a non-monotonic behavior of $\eta$ with temperature.