Non-Abelian hydrodynamics and the flow of spin in spin-orbit coupled substances

TL;DR

This paper explores the hydrodynamic behavior of non-Abelian spin systems in condensed matter, revealing new phenomena like spin flow classification, fragility of non-Abelian effects, and the restoration of hydrodynamics by order parameters.

Contribution

It introduces a unifying framework for non-Abelian spin transport, highlighting the role of quantum entanglement and order parameters in hydrodynamics.

Findings

Non-Abelian currents can be separated into classical and quantum entangled parts.

Non-Abelian transport phenomena are more fragile than Abelian counterparts.

Order parameters restore hydrodynamics and enable new effects like charge trapping.

Abstract

Motivated by heavy ion collision experiments, we study the hydrodynamic properties of non-Abelian systems. These issues arise in condensed matter physics in the context of transport of spins in the presence of spin orbit coupling: the Pauli Hamiltonian governing the leading relativistic corrections in condensed matter systems can be rewritten in a language of SU(2) covariant derivatives, where the role of the non-Abelian gauge fields is taken by the physical electromagnetic fields. Taking a similar perspective as Jackiw and coworkers, we show that non-abelian hydrodynamical currents can be factored in a non-coherent 'classical' part, and a coherent part requiring macroscopic non-abelian quantum entanglement. Non-abelian flow being thus a much richer affair than familiar hydrodynamics, permits us to classify the various spin transport phenomena in in condensed matter physics in a unifying framework.In semiconductor spintronics, the absence of hydrodynamics is well known, but in our formulation it is directly associated with the fact that non-abelian currents are only covariantly conserved.We analyze the quantum mechanical single particle currents of relevance to mesoscopic transport with as highlight the Aharonov-Casher effect, where we demonstrate that the non-abelian transport structure renders it much more fragile than its abelian counterpart, the Aharonov-Bohm effect. We subsequently focus on spin flows protected by order parameters, of which the spin-spiral magnets and the spin superfluids are important examples. The surprising bonus is that the presence of an order parameter, being single-valued, restores hydrodynamics. We demonstrate a new effect: the trapping of electrical line charge, being the 'fixed frame' non-Abelian analogue of the familiar magnetic flux trapping by superconductors.