Hubbard model for intermediate-dimensional excitons.

Abstract

A Hubbard model is solved exactly to characterize confined, intermediate-dimensional excitons for the full range of electron and hole hopping and interaction strengths. Finite systems with periodic boundary conditions model unconfined excitons. Finite systems with terminated ends model confined excitons. Exciton energies, oscillator strengths, and electron and hole distributions are determined. Oscillator strengths and electron-hole distributions of confined intermediate-dimensional excitons exhibit anomalous, nonmonotonic, nonuniversal dependences on the electron-hole interaction strength and hopping that are counter to the conventional behavior for quantum-confined excitons and free excitons. Perturbation theory is used to clarify the weak and large interaction limits. In the large-interaction limit, an exciton dead layer occurs near the boundary of the system because electron-hole correlation is suppressed near the boundary. Second-order perturbation theory determines the surface potential barrier caused by the suppression of pair correlation near the surface and determines the hopping rate for tunneling into this barrier. In the weak-interaction limit, on-site correlation of a confined electron-hole pair is suppressed by asymmetry in the electron and hole hopping. For large asymmetry in the electron and hole hopping, the oscillation strength of the confined intermediate-dimensional exciton can be less than the oscillator strength of an uncorrelated, noninteracting pair.