Density functional theory based calculation of small-polaron mobility in hematite

The mobility of electron small polarons in hematite, $\ensuremath{\alpha}$-${\text{Fe}}_{2}$${\text{O}}_{3}$, is calculated by density functional theory within the generalized gradient approximation including Hubbard $U$ corrections. Our work goes beyond previous computational investigations of this system by computing both the prefactor and activation energies for adiabatic polaron transport. The results obtained using a Hubbard $U$ value of 4.3 eV yield a calculated value of the room-temperature basal plane mobility of 0.009 S*${\text{cm}}^{2}$/s, which compares to within an order of magnitude with experimental measurements. Further, the values of the electronic-coupling parameter in the Marcus theory for small-polaron transport are estimated from DFT$\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}U$ calculations of the defect energy levels in the stable and saddle-point configurations. Our results predict an adiabatic polaron transfer, in good agreement with previous wave function based calculations.