Flux Quantization Due to Monopole and Dipole Currents

By discussing field-induced quantum interference effects due to monopole moments and those due to dipole moments on equal footing, their similarities and differences are clarified. First, we demonstrate the general principle for flux quantization. For particles carrying a monopole moment, the interference causes monopole current to oscillate periodically with flux defined as inner product of field and area, whereas for particles carrying a fixed dipole moment, the dipole current oscillates periodically with flux vector defined as cross product of field and trajectory. Our analysis unifies the oscillation of monopole or dipole currents in various devices, such as SQUID and spin-FET, into the same physical picture. Second, we show that interference effects can also happen in open trajectory devices that transport dipole currents, such as spin Josephson effect, based on the non-gauge field nature of the interference effects of dipole moments. In addition, we propose that the interference effect of electric dipoles, known as He-McKellar-Wilkens effect, can be realized by the bilayer exciton condensates observed in semiconductor heterostructure and bilayer graphene.