Electromagnetic response in dipole superfluids: vortex lattices and singular domain walls

Among the most significant macroscopic quantum phenomena in condensed matter physics is the Meissner effect observed in superconductivity, which arises from the unique interaction between superfluids of charged particles and electromagnetic fields. However, superfluids can also emerge from particles possessing distinct electromagnetic properties. In particular, there has been growing interest in superfluids composed of charge-neutral particles with magnetic or electric dipole moments, such as Bose-Einstein condensates of magnons or excitons. Despite this interest, the electromagnetic response of dipole superfluids, including potential analogs or contrasts to the Meissner effect, remains poorly understood. In this work, we develop a Ginzburg-Landau phenomenological theory to describe magnetic and electric dipole superfluids subjected to pseudo-magnetic fields induced by geometric phases. For magnetic dipole superfluids interacting with the Aharonov-Casher (AC) phase, we find that they form vortex lattices with sharply localized pseudo-magnetic fields along hexagonal domain walls, leading to singular and discontinuous change of physical variables at these boundaries. For electric dipole superfluids influenced by the He-McKellar-Wilkens (HMW) phase, in contrast, we identify vortex lattices where the pseudo-magnetic field and supercurrent are concentrated at vortex cores, resembling superconductors. These results reveal strikingly different electromagnetic responses in dipole superfluids, opening new directions for exploring superfluid systems with unconventional electromagnetic responses.