Frenkel-like Wannier-Mott Excitons in Few-Layer PbI2
  Optical measurements and first-principles calculations of the band structure and exciton states in direct-gap bulk and few-layer PbI2 indicate that the n = 1 exciton is Frenkel-like in nature in that its energy exhibits a weak dependence on thickness down to atomic-length scales. Results reveal large increases of the gap and exciton binding energy with decreasing number of layers, and a transition of the fundamental gap, which becomes indirect for 1-2 monolayers. Calculated values are in reasonable agreement with a particle-in-a-box model relying on the Wannier-Mott theory of exciton formation. General arguments and existing data suggest that the Frenkel-like character of the lowest exciton is a universal feature of wide-gap layered semiconductors whose effective masses and dielectric constants give bulk Bohr radii that are on the order of the layer spacing. 
Alexis S. Toulouse, Benjamin P. Isaacoff, Guangsha Shi, Marie   Matuchov\'a, Emmanouil Kioupakis and Roberto Merlin
cond-mat.mes-hall