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Non-Abelian electromagnetism in Josephson junctions :

spin accumulation, spin currents, magneto-electric and spin galvanic effects, anomalous phase-shift


The combination of spin-orbit interaction and superconducting correlation has attracted more and more interests over the last years. One reason is the possibility to generate the topological superconducting regime, when unpaired Majorana modes emerge naturally at the edges of 1D wires. However, the understanding of the complete phenomenology associated to these systems requires further elaborations. The goal of this presentation is to explore a few spin and charge phenomenology of superconducting hetero- structures outside the topological regime.
A modern version of the quasi-classic and transport equations will be presented, when charges and spin degrees of freedom are accounted for on the same footing, generalizing the covariant gradient expansion towards its non-Abelian sector. The resulting equations and observables exhibit intrinsic charge and spin coupling, leading to some magneto-electric effects. One of such spin-Hall-like effects is the Edelstein one, predicted to exist in polar superconductivity. In a bulk superconductor, it results a generation of a spin-polarization by a biased current. The inverse Edelstein effect, or spin-galvanic effect, corresponds to the generation of a phase gradient when a spin-splitting field applies to a superconductor with spin-orbit coupling. The corresponding phenomenology in systems with proximity effect will be elucidated, with particular emphasis on the generation of an anomalous phase-shift in Josephson junctions.

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