One-dimensional nexus objects, network of Kibble-Lazarides-Shafi string walls, and their spin dynamic response in polar-distorted B-phase of 3He

The domain wall problem in the axion solution of strong CP violation has condensed-matter-based analogy in nafen-distorted superfluid 3He. The Kibble-Lazarides-Shafi (KLS) domain wall, which appears during the temperature of the early universe cooling down to QCD scale, attaches to the string defect that appeared in the first time symmetry breaking phase transition. Recent experiments in rotating superfluid 3He produced the network of the KLS string walls in a human controllable system. In this system, the half quantum vortices (HQVs) appear the first time symmetry breaking from a normal phase vacuum to a polar phase, while the KLS domain walls appear and attach on the HQVs in the phase transition from the polar phase to polar-distorted B-phase. Based on the method of relative homotopy group, the KLS string walls have turned out to be the descendants of HQVs of the polar phase. Here we further show the KLS string walls smoothly connect to spin solitons with a length scale around ξD when the spin orbital coupling is taken into account. This means HQVs are one-dimensional (1D) nexuses, which connect the spin solitons and the KLS domain walls. This is because the subgroup G=π1(S1S,˜R2) of relative homotopy group describing the spin solitons is isomorphic to the group describing the half spin vortices—the textures of the spin degree of freedom of the KLS string wall. In the nafen-distorted 3He system, 1D nexus objects and the spin solitons with topological invariant 2/4 have two different types of networks, which are named as pseudorandom lattices of inseparable and separable spin solitons. These two types of pseudorandom lattices correspond to two different representations of G. We discuss the condition under which the pseudorandom lattice model works. The equilibrium configuration and surface densities of free energies of pseudorandom lattices are calculated by numeric minimization. Based on the equilibrium spin textures, we calculate their transverse spin dynamic response of NMR, the resulted frequency shifts, and√Ω scaling of the ratio intensity exactly coincide with the experimental measurements. We also discuss the mirror symmetry in the presence of the KLS domain wall and its explicit breaking. Our discussions and considerations can be applied to the composite defects in other condensed matter and cosmological systems.Peer reviewe