Absence of magic fillings of carrier-doped C₆₀ in a field-effect transistor

Motivated by recent experiments of carrier-doped C$_{60}$ in a field-effect transistor (FET), effects of spatial single particle potential variations on Mott-Hubbard (MH) insulators are studied theoretically. It is shown that the presence of strong random potentials leads to a reduced dependence of electronic properties on band fillings and to disappearance of the MH insulating behavior at integer fillings. A simple physical picture to explain this behavior is given using a notion of self-doping of the MH insulator. Our results have important implications on some of the puzzling observations of carrier-doped C$_{60}$ in the FET. It is also discussed that the FET configuration with Al{$_2$}O{$_3$} dielectric provides an ``ideal'' system with strong disorders.