Two interacting charged particles in an Aharonov-Bohm ring: Bound state transitions, symmetry breaking, persistent currents, and Berry’s phase

By using a Green's function procedure we determine exactly the energy spectrum and the associated eigenstates of a system of two oppositely charged particles interacting through a contact potential and moving in a one-dimensional ring threaded by a magnetic flux. Critical interactions for the appearance of bound states are analytically determined and are viewed as limiting cases of many-body results from the area of interaction-induced metal-insulator transitions in charged quantal mixtures. Analytical expressions on one-body probability and charge current densities for this overall neutral system are derived and their single-valuedness leads to the possibility of states with broken symmetry, with possible experimental signatures in exciton spectra. Persistent currents are analytically determined and their properties investigated from the point of view of an interacting mesoscopic system. A cyclic adiabatic process on the interaction potential is also identified, with the associated Berry's phase directly linked to the electric (persistent) currents, the probability currents having no contribution for a neutral system.