Composite topological objects in topological superfluids

Abstract

Superfluid phases of $^3$He discovered in 1972 opened the new area of the application of topological methods to condensed matter systems. Due to the multi-component order parameter which characterizes the broken $SO(3)\times SO(3)\times U(1)$ symmetry in these phases, there are many inhomogeneous objects -- textures and defects in the order parameter field -- which are protected by topology and are characterized by topological quantum numbers. Among them there are quantized vortices, skyrmions and merons, solitons and vortex sheets, monopoles and boojums, Alice strings, Kibble-Lazarides-Shafi walls terminated by Alice strings, spin vortices with soliton tails, etc. Most of them have been experimentally identified and investigated using nuclear magnetic resonance (NMR) techniquie, and in particular the phase coherent spin precession discovered in 1984 in $^3$He-B by Borovik-Romanov, Bunkov, Dmitriev and Mukharskiy in collaboration with Fomin.