NONINTEGER FLUX QUANTA FOR A SPHERICAL SUPERCONDUCTOR

A thin-film superconductor shaped into a spherical shell at whose cent er lies the end of long thin solenoid in which there is an integer flu x N Phi(0) has been previously extensively studied numerically as a mo del of a two-dimensional superconductor. The emergent Aux from the sol enoid produces a radial B field at the superconducting shell and N vor tices in the superconducting film We study here the effects of includi ng a second solenoid (carrying a flux f) which is inserted inside the first solenoid but passing right across the sphere. This Aharonov-Bohm (AB) flux does not have to be quantized to make the order parameter s ingle valued. The Ginzburg-Landau free energy is minimized at fixed N as a function off and it is found that the minimum is usually achieved when the AB flux f is half a flux quantum, but depending on N the min imum may be at f = 0 or values which are not obvious rational fraction s. [S0163-1829(98)01114-X].