A toy model to investigate the existence of excitons in the ground state of strongly-correlated semiconductor

Excitons, quasiparticles associated with bound states between an electron and a hole and are typically created when photons with a suitable energy are absorbed in a solid-state material. We propose to study a possible emergence of excitons, created not by photon absorption but the effect of strong electronic correlations. This study is motivated by a recent experimental study of a substrate material SrTiO₃ (STO) that reveals strong exitonic signals in its optical conductivity. Here we conjecture that some excitons may already exist in the ground state as a result of the electronic correlations before the additional excitons being created later by photon absorption. To investigate the existence of excitons in the ground state, we propose to study a simple 4-energy-level model that mimics a situation in strongly-correlated semiconductors. The four levels are divided into two groups, lower and upper groups separated by an energy gap, E_g , mimicking the valence and the conduction bands, respectively. Further, we incorporate repulsive Coulomb interactions between the electrons. The model is then solved by exact diagonalization method. Our result shows that the toy model can demonstrate band gap widening or narrowing and the existence of exciton in the ground state depending on interaction parameter values.