Geometry controlled superconducting diode and anomalous Josephson effect triggered by the topological phase transition in curved proximitized nanowires

We study the key features of the Josephson transport through a curved semiconducting nanowire. Based on numerical simulations and analytical estimates within the framework of the Bogoliubov-de Gennes equations we find the ground-state phase difference \(\varphi_0\) between the superconducting leads tuned by the spin splitting field \(h\) driving the system from the topologically trivial to the nontrivial superconducting state. The phase \(\varphi_0\) vanishes for rather small \(h\), grows in a certain field range around the topological transition, and then saturates at large \(h\) in the Kitaev regime. Both the subgap and the continuum quasiparticle levels are responsible for the above behavior of the anomalous Josephson phase. It is demonstrated that the crossover region on \(\varphi_0(h)\) dependencies reveals itself in the superconducting diode effect. The resulting tunable phase battery can be used as a probe of topological transitions in Majorana networks and can become a useful element of various quantum computation devices.