Fractional charge, spin and statistics of solitons in superfluid3He film

Abstract

The topological Chern-Simons term with the parameter theta =n pi exists in the superfluid 3 He-A thin film, where an integer parameter n may be odd or even depending on the thickness of the film. The particle like soliton in 3 He-A film (so-called skyrmion) with integer topological charge Q has spin s=nQh(cross)/2 and obeys Fermi-Dirac quantum statistics at odd Q and n. The topological term in action leads to specific quantised Hall effect for spin current in 3 He-A. In the planar phase of the 3 He film the non-singular 4 pi spin disclination has the fractional fermion charge 1 / 2 n which corresponds to the fractional electric charge 1 / 2 en for the disclination in the planar state superconductor. The spin disclination in the 3 He-A 1 film has both the fractional spin 1 / 4 h(cross)n and fractional charge 1 / 4 n.