  Lithium titanium oxide Li$_4$Ti$_5$O$_{12}$ (LTO) is an intriguing anode
material promising particularly long lived batteries, due to its remarkable
phase stability during (dis)charging of the cell. However, its usage is limited
by its low intrinsic electronic conductivity. Introducing oxygen vacancies can
be one method to overcome this drawback, possibly by altering the charge
carrier transport mechanism. We use Hubbard corrected density-functional theory
(DFT+U) to show that polaronic states in combination with a possible hopping
mechanism can play a crucial role in the experimentally observed increase of
electronic conductivity. To gauge polaronic charge mobility, we compute
relative stabilities of different localization patterns and estimate polaron
hopping barrier heights. With this we finally show how defect engineering can
indeed raise the electronic conductivity of LTO up to the level of its ionic
conductivity, thereby explaining first experimental results for reduced LTO.
