Singular and Non-singular Vortices and Their Excitation Spectra of Neutral Fermi Superfluids in Restricted Geometries

We study stable vortices and their bound excitation spectra in superfluid He-3-A phase under restricted geometries. By choosing appropriate geometry we can control the (l) over right arrow -vector and (d) over right arrow -vector of the A phase order parameter (OP), making it possible to select a particular vortex among a variety of singular or non-singular vortices. This tunability through the boundary condition and external field is demonstrated to be useful. Here we take up two examples of the restricted geometries under rotation: A narrow cylinder whose radius is 50 mu m under field parallel to the rotation axis and thin film configuration sandwiched by parallel plates whose gap is an order of mu m or less. We examine the ongoing experiment by rotating cryostat at ISSP, University of Tokyo, reporting on new vortex state for a cylinder in a slow rotation speed region near T-c. For parallel plates in a field parallel to the film surface we analyze the conditions under which singular vortex is stable. This study allows us to examine experimental realization of so-called Majorana zero energy state bound in a core in He-3-A chiral phase.