Magnetically-active Boundaries in Topological Superfluid 3He-B

We calculate properties of the BW phase of superfluid Helium-3 near magnetically-active boundaries using quasiclassical theory. The quasiparticles acquire spin-dependent phase shift when scattering off such surfaces. This local breaking of the time-reversal symmetry by the boundary is sufficient to remove the topological protection of the surface zero-energy Majorana modes. We investigate how magnetic scattering affects the order parameter structure, surface density of states and helical surface spin currents. In He-B the spin and orbital degrees of freedom are connected by the broken relative spin-orbit rotational symmetry, and magnetic boundaries can provide a more flexible control of the surface bound states. In particular, we show that such boundaries strongly affect superfluid phases in confined geometry, such as slabs with thickness of several coherence length.