Majorana fermions bound at vortices and surface of superfluid ³He

We investigate the Majorana fermions bound at vortices and specular surface of superfluid ³He A- and B-phases. It is demonstrated that the statistics of the integer vortex which is competitive to the half-quantum vortex is sensitive to the orientation of the magnetic field. We also discuss the surface Andreev bound state in the B-phase, which is expected to behave as Majorana fermions at the zero field limit. Based on the quasiclassical and Bogoliubov-de Gennes theories, we clarify that in the presence of the magnetic field parallel to the surface, the stable configuration of the -vector, which reflects the spin-orbit symmetry breaking, traces the point at which the surface state has the maximum gap.