Sharp transitions in the spectra of small Frenkel-like excitons for multi-orbital lattice systems

Abstract

We propose a method for calculating exciton spectra and wavefunctions for model lattice Hamiltonians, based on real-space electron-hole propagators. We verify that our results agree with those of the continuum approximation in the limit of large Wannier excitons, and propose a simple criterion to estimate the exciton size above which the continuum approximation is quantitatively accurate. We then investigate simple one- and two-dimensional multi-orbital lattice models and show that small, Frenkel-like excitons, whose size approaches the lattice constant, can display physics that disagrees with the simplest continuum descriptions (a single-valley quadratic expansion around the minimum gap) not just quantitatively, but qualitatively. Specifically, we identify sharp transitions in the character and momentum of the lowest-energy exciton, enabled by the multi-orbital nature of the lattice models.