Excitons in Multi-Orbital Lattice Models

Inorganic semiconductors such as silicon typically host Wannier-Mott excitons with small exciton binding energy (comparable to or smaller than room temperature). Because of the large average separation between the electron and hole, continuum models are often sufficiently accurate to describe these weakly-bound states. However, in organic materials with significantly weaker screening, such as C60 films, excitons become very tightly bound and have very large binding energies. Here, continuum models may not accurately capture the exciton dispersion. To gauge their accuracy, we study one- and two-dimensional multi-orbital lattice models with a variety of electron-hole attraction potentials. We calculate exactly the resulting exciton dispersion and compare them to those predicted by continuum models, offering new insights into both the behavior of strongly-bound excitons, and on the limits of validity of the continuum approximation.