Non-reciprocal phenomena in diffusive superconducting structures with spin-orbit coupling

The search for non-reciprocal transport in superconductors is a recent topic of major interest. Breaking both time-reversal and inversion symmetries in a superconducting system yields a plethora of magnetoelectric phenomena. The most notable example is the recently discovered supercurrent diode effect, which shows up via non-reciprocal current flow: supercurrent can flow in one direction, whereas only a regular dissipative current can flow in another. Another example is the anomalous phase shift in Josephson junctions. Beyond technological interest, the magnetoelectric phenomena provide a way to probe microscopic properties of the material by transport measurements, particularly the spin-orbit coupling strength. In the first part of the talk, we will present an overview and a simple phenomenological theory of non-reciprocal phenomena in systems with spin-orbit coupling. In the second part, we will present a powerful tool to microscopicaly model these effects – the quasiclassical (Usadel) formalism, which is suitable for description of diffusive and hybrid systems. We will discuss our numerical package for solving the Usadel equation, which enables to study non-reciprocal phenomena for a wide variety of superconducting systems.