Exciton in an Aharonov–Bohm ring: an exactly soluble interacting mesoscopic system

Abstract

A Green's function procedure leads to an exact determination of 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. We obtain analytical criteria for transitions from excited to bound states and compare with 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 are derived and their single-valuedness leads to states with broken symmetry, with possible experimental consequences in exciton physics. 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, a result generalized to non-neutral cases with the probability current also playing a role.