Core structure and dynamics of non-Abelian vortices in a biaxial nematic spinor Bose-Einstein condensate

We demonstrate that multiple interaction-dependent defect core structures as well as dynamics of \emph{non-Abelian} vortices can be realized in the biaxial nematic (BN) phase of a spin-2 atomic Bose-Einstein condensate (BEC). An experimentally simple protocol may be used to break degeneracy with the uniaxial nematic phase. We show that a discrete \emph{spin-space symmetry} in the core may be reflected in a breaking of its \emph{spatial symmetry.} The discrete symmetry of the BN order parameter leads to non-commuting vortex charges. We numerically simulate reconnection of non-Abelian vortices, demonstrating formation of the obligatory \emph{rung vortex.} In addition to atomic BECs, non-Abelian vortices are theorized in, e.g., liquid crystals and cosmic strings. Our results suggest the BN spin-2 BEC as a prime candidate for their realization.