Topological interfaces and vortex splitting instabilities in spin-2 Bose-Einstein condensates

Interfaces connecting topologically distinct phases of a physical system are phenomena of interest in several contexts, from condensed matter to early-universe cosmology. Optically trapped Bose-Einstein condensates with spin degrees of freedom (spinor BECs) provide an experimental testbed to observe topological defects and their dynamical stability. In this work, we study defect connections throughout topological interfaces in spin-2 BECs, where the rich variety of order-parameter symmetries allows for fractional non-Abelian vortex charges. We demonstrate the existence of fractional vortex connections in uniaxial-to-biaxial nematic (UN-BN), cyclic-to-ferromagnetic (C-FM), and cyclic-to-biaxial nematic (C-BN) interfaces. Moreover, we characterize intriguing core deformations along connections involving higher-order defects such as monopoles and coreless vortices. Finally, we develop a semi-analytical tool to predict vortex instabilitities in terms of an interplay of ground-state phases. We provide evidence of its convenience by numerically solving the Bogoliubov-deGennes (BdG) equations, leading to an easier interpretation of unstable vortex excitations occurring at the topological interface between two phases of a spin-2 BEC.