Interplay of charge and vorticity quantization in superconducting Coulomb blockaded island

The angular momentum or vorticity of Cooper pairs is shown to affect strongly the charge transfer through a small superconducting (S) island of a single electron transistor. This interplay of charge and rotational degrees of freedom in a mesoscopic superconductor occurs through the effect of vorticity on the quantum mechanical spectrum of electron-hole excitations. The subgap quasiparticle levels in vortices can host an additional electron, thus, suppressing the so-called parity effect in the S island. We propose to measure this interaction between the quantized vorticity and electric charge via the charge pumping effect caused by alternating vortex entry and exit controlled by a periodic magnetic field.