Trimeron ordering, bandgap, and polaron hopping in magnetite

In this work, we apply the $\text{DFT}+U$ approach for a detailed ab initio study of the refined structure of the low-temperature phase of magnetite [M. S. Senn et al., Nature (London) 481, 173 (2012)]. We compare the electronic properties of this structure and several alternatives with respect to the presence of trimeron ordering and the bandgap properties. The connection of the trimeron arrangement with site-selective doping of magnetite is discussed. Calculations of the polaron hopping energy allow us to make one step forward toward understanding the complex interplay of polaronic and bandgap contributions to electronic properties of the magnetite.