The pressure variation in the structural parameters, $u$ and $c/a$, of the delafossite ${\text{CuAlO}}_2$ is calculated within the local-density approximation (LDA). Further, the electronic structures as obtained by different approximations are compared: LDA, $\text{LDA}+U$, and a recently developed “quasiparticle self-consistent $GW$”$\left(\text{QS}GW\right)$ approximation. The structural parameters obtained by the LDA agree very well with experiments but, as expected, gaps in the formal band structure are underestimated as compared to optical experiments. The (in LDA too high lying) $\text{Cu}3d$ states can be down shifted by $\text{LDA}+U$. The magnitude of the electric field gradient (EFG) as obtained within the LDA is far too small. It can be “fitted” to experiments in $\text{LDA}+U$ but a simultaneous adjustment of the EFG and the gap cannot be obtained with a single $U$ value. $\text{QS}GW$ yields reasonable values for both quantities. LDA and $\text{QS}GW$ yield significantly different values for some of the band-gap deformation potentials but calculations within both approximations predict that $3R{\text{-CuAlO}}_2$ remains an indirect-gap semiconductor at all pressures in its stability range 0–36 GPa, although the smallest direct gap has a negative pressure coefficient.

• Received 7 August 2009

DOI:https://doi.org/10.1103/PhysRevB.81.045203