Novel π-type vortex in a nanoscale extreme type-II superconductor: Induced by quantum-size effect

By numerically solving the Bogoliubov-de Gennes equations, we report a novel π-type vortex state whose order parameter near the core undergoes an extraordinary π-phase change for a quantum-confined extreme type-II s-wave superconductor. Its supercurrent behaves as the cube of the radial coordinate near the core, and its local density of states spectrum exhibits a significant negative-shifted zero-bias peak. Such π-type vortex state is induced by quantum-size effect, and can survive thermal smearing at temperatures up to a critical value Tτ. The Anderson's approximation indicates that the π-type vortex may remain stable under sufficiently week magnetic field in the case less deep in the type-II limit. Moreover, we find that its appearance is governed by the sample size and kFξ0 with kF the Fermi wave number and ξ0 the zero-temperature coherence length. Similar effects may be expected in quantum-confined ultracold superfluid Fermi gasses, or even high-Tc superconductors with proper kFξ0 value.