Excitonic polarons in confined systems

Abstract

We derive explicit analytical expressions for the ground state excitonic polaron (energy, effective mass) using the fractional-dimensional space formalism. Our results are shown to provide a wider overview of the character of the excitonic polaron than the analysis performed using integral dimensions only. We include a derivation of the energy difference between the 1s and 2s states as well as the phonon Lamb shift (energy difference between the 2p and 2s states) in simple analytical forms. Our results compare well with experimental data and earlier theoretical estimates for a variety of different material systems. We extend the fractional-dimensional model to analyse excitonic polarons in coupled double quantum wells and quantum disc systems.