Topological hydrodynamics in ferromagnetic superconductors

Abstract

We explore the physical consequences of enriching the U(1) order parameter of conventional superconductors to a more topologically featureful space. As an illustrative case study, we focus on fully spin-polarized triplet superconductors, which are underlied by the SO(3) d-vector order parameter. We find that a bulk-edge correspondence links the circulation of supercurrent to the bulk magnetic skyrmions, giving rise to topological hydrodynamics of magnetic skyrmions. To probe the interplay of charge and spin dynamics, we propose a blueprint for a spin-triplet superconducting quantum interference device (SQUID), which functions without a Josephson weak link. The triplet SQUID undergoes nonsingular 4π phase slips, in which current relaxation is facilitated by spin dynamics that trace out a magnetic skyrmion texture. Inductively coupling the device to a tank circuit and probing the nonlinear supercurrent response via Oersted field measurements could provide an experimental signature of ferromagnetic spin-triplet superconductivity. Finally, we develop a general Poisson bracket formalism to describe the intertwined spin and charge dynamics such that all topological constraints are preserved, even in the presence of dissipation.

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