There were two PL bands, centered at 400 nm (band A) and 425 nm (band B). Band A was most dominant in the sulfur-deficient sample and hence associated with a sulfur vacancy, while band B was dominant in the indium-rich sample and hence linked with indium interstitials.
It seems you and Yuri may have had other discussions not published here, as the document I opened only shows one spectrum without additional notes. Please clarify as additional information can help.
Without additional information about the nanoparticle synthesis, one could assign the observed PL features to size distributions of your nanoparticles. That is, each peak/band could represent groupings of nanoparticle sizes, which then modifies the energy levels within the np's. Can you characterize the np sizes (for example by TEM, SEM, small-angle X-ray scattering, etc)? How are you exciting the np's for your PL measurements?
Regarding your experiment, are the nanoparticles in solution (colloidal)? Optical absorption measurements could provide valuable insight into band structure.