Anyon pairing via phonon-mediated interaction

Abstract

In this paper, we study the pairing of anyons subjected to an external uniform magnetic field and confined in a two-dimensional parabolic quantum dot within the framework of Fr\ohlich large bipolaron theory, motivated by the Wilczek's prescription that treats anyons as composites having both charges and fictitious flux tubes. In this model, electrons bound to Aharanov-Bohm type flux tubes and surrounded by a cloud of virtual LO phonons interact with each other through the long range Coulomb and statistical potentials. In order to discuss the effects of both spatial confinement potential and external uniform magnetic field on the boundaries of the stability region of such a pairing in real space, we perform a self-consistent treatment of the ground-state energies of both an interacting anyon pair and two noninteracting anyons. Our results suggest that two interacting anyons can be bound into a condensate anyon pair through a phonon-mediated interaction.