In nano material,  the electronic bands is suffering from less broadening than bulk due to less interactions between particles, molecules, atoms.

in oxides the bond metal-oxygen is responsible for energy gap compared to metal-metal bond in metals. As I think, the density does not play the main role in variation of the gap.

Broadening and narrowing of band gap in metal oxides semiconductors are extensively influenced by doping. The energy of band gap depends on the interactions of the guest(dopant) and host material(metal oxide). Doping formed a new energy levels which causes a decreasing in band gap energy value.

Doping with donor impurities create energy levels in the band gap near the conduction band edge while doping with acceptor impurities create energy levels near the valence band edge. As the percentage of doped material increases the energy of band gap continues to decrease.

Fundamentally, we know of electrons to be tightly bound close to the nucleus (core), or to exist in the valence band which is further away from the nucleus or even further than that in the conduction band where are not free to roam around freely. So the band gap is determined by the energy needed for the electrons to migrate from the valence band to the conduction band. This band gap is characteristic to each element, since the electron energy levels and states are all characteristic to each element as well.

However, when we consider band gap in bulk phase, it no longer has to be characteristic of the element. It then becomes dependent on the choice of dopant/impurity as well as the concentration of dopant/impurity.