Magnetite
exhibits a famous phase transition, called Verwey transition,
at the critical temperature TV of about
120 K. Although numerous efforts have been devoted to the understanding
of this interesting transition, up to now, it is still under debate
whether a charge ordering and a band gap exist in magnetite above TV. Here, we systematically investigate the charge
ordering and the electronic properties of magnetite in its cubic phase
using different methods based on density functional theory: DFT+U
and hybrid functionals. Our results show that, upon releasing the
symmetry constraint on the density but not on the geometry, charge
disproportionation (Fe2+/Fe3+) is observed,
resulting in a band gap of around 0.2 eV at the Fermi level. This
implies that the Verwey transition is probably a semiconductor-to-semiconductor
transition and that the conductivity mechanism above TV is small polaron hopping.