From the tight-binding picture of insulators, the band-gaps arise from the intrinsic energy differences between atomic orbitals energy levels. The largest I have found so far is roughly 10eV (amorphous SiO2). Of course this picture doesn't always apply, you can have insulating behavior from electron-electron correlations (e.g. a Mott insulator). However, for the most part, Mott gaps tend to be less than a few electron volts, so I am ignoring them.
My questions are the following:
- Is there a physical upper limit to the band-gap of insulators in general? What about the case where the constituents are specified?
- If there is such a limit, what is the smallest it could possibly be?
- What is the largest band-gap of a known material/system?
Naively, one could place an upper bound on the band-gap for a given system by looking at the largest energy difference between the underlaying atomic orbitals. However the number you get with this method tends to be quite large, so I feel that one could do much, much better than this.