Unconventional aspects of electronic transport in delafossite oxides

The electronic transport properties of the delafossite oxides ABO$_2$ are usually understood in terms of two well separated entities, namely, the triangular A$^+$ and (BO$_2$)$^-$ layers. Here we review several cases among this extensive family of materials where the transport depends on the interlayer coupling and displays unconventional properties. We review the doped thermoelectrics based on CuRhO$_2$ and CuCrO$_2$, which show a high-temperature recovery of Fermi-liquid transport exponents, as well as the highly anisotropic metals PdCoO$_2$, PtCoO$_2$ and PdCrO$_2$ where the sheer simplicity of the Fermi surface leads to unconventional transport. We present some of the theoretical tools that have been used to investigate these transport properties and review what can and cannot be learned from the extensive set of electronic structure calculations that have been performed.