I assume those "quantum oscillation" measurements were electron cyclotron resonance measurements[1]. Also there is an other type of non-conventional insulator

I assume those "quantum oscillation" measurements were electron cyclotron resonance measurements[1]. Also there is an other type of non-conventional insulator which is considered to be well understood: the Mott-insulator[2]. It really doesn't fit in here as a candidate since one wouldn't expect cyclotron resonance from this model in the insulating regime. However it's a good learning example of strongly correlated electrons in materials. [1]https://en.wikipedia.org/wiki/Electron_cyclotron_resonance#In_condensed_matter_physics https://en.wikipedia.org/wiki/Electron_cyclotron_resonance#I... [2]https://en.wikipedia.org/wiki/Mott_insulator https://en.wikipedia.org/wiki/Mott_insulator