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 ³He-A phase under restricted geometries. By choosing appropriate geometry we can control the -vector and -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 μm under field parallel to the rotation axis and thin film configuration sandwiched by parallel plates whose gap is an order of μm 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 ³He-A chiral phase.