  Acceptor-doped perovskite oxides like BaZrO$_3$ are showing great potential
as materials for renewable energy technologies where hydrogen acts an energy
carrier, such as solid oxide fuel cells and hydrogen separation membranes.
While ionic transport in these materials has been investigated intensively, the
electronic counterpart has received much less attention and further exploration
in this field is required. Here, we use density functional theory (DFT) to
study hole polarons and their impact on hole conductivity in Y-doped BaZrO$_3$.
Three different approaches have been used to remedy the self-interaction error
of local and semi-local exchange-correlation functionals: DFT$+U$, pSIC-DFT and
hybrid functionals. Self-trapped holes are found to be energetically favorable
by about $-$0.1 eV and the presence of yttrium results in further
stabilization. Polaron migration is predicted to occur through intraoctahedral
transfer and polaron rotational processes, which are associated with adiabatic
barriers of about 0.1 eV. However, the rather small energies associated with
polaron formation and migration suggest that the hole becomes delocalized and
band-like at elevated temperatures. These results together with an endothermic
oxidation reaction [A. Lindman et al., Phys. Rev. B 91, 245114 (2015)] yield a
picture that is consistent with experimental data for the hole conductivity.
The results we present here provide new insight into hole transport in
acceptor-doped BaZrO$_3$ and similar materials, which will be of value in the
future development of sustainable technologies.
