Excitonic-dimer model with oscillatory Fano damping

Abstract

The dynamical properties of an excitonic dimer coupled to a harmonic oscillator are analysed as a simple model for the problem of self-localization of excitons in crystalline systems. If the oscillator is treated classically and a damping term is included in a phenomenological way, the system relaxes to its lowest-energy state, which is either a symmetrical or a site-trapped, symmetry-broken state depending on the values of the system parameters. By quantum mechanical analysis, employing the accurate eigensolutions of the system obtained in previous work, it is possible to establish a semi-quantitative argument suggesting that this symmetry-breaking behaviour is an artifact of the semiclassical approximation. This argument is based, on the one hand, on group theoretical requirements and, on the other, on the exploitation of a Fano-type model for the coupling of the local oscillator to a bath. An illustration is made for the down-cascading of the excitonic energy to the final state.