Anomalous Compressibility and Electronic Robustness of Metallic Delafossite PdCoO$_2$ under Pressure

The layered delafossite PdCoO$_2$ is an exceptional oxide metal whose ultrahigh conductivity arises from a Pd-derived nearly-free-electron band. Here, high-pressure single-crystal X-ray diffraction combined with first-principles calculations is used to investigate its structural, bonding, and electronic evolution up to 10 GPa. PdCoO$_2$ retains the rhombohedral R-3m structure throughout the investigated pressure range, with no structural phase transition. The lattice exhibits an unusual anisotropic compression, with the in-plane a-axis contracting more strongly than the stacking c-axis, opposite to the behavior of most layered materials. Despite this anomalous compressibility, only minor changes are observed in the local Pd-O and Co-O coordination environments, indicating a remarkably rigid bonding framework. Crystal orbital Hamilton population analysis reveals only subtle strengthening of the existing bonding interactions, without the emergence of destabilizing Pd-related antibonding states. Consistent with these findings, the Pd-derived metallic band and quasi-two-dimensional Fermi surface remain essentially unchanged under compression. Boltzmann transport calculations further show that the in-plane conductivity is nearly pressure-independent, whereas the out-of-plane conductivity decreases modestly, resulting in a slight increase in transport anisotropy. These results demonstrate that the anomalous compressibility of PdCoO$_2$ originates from its robust chemical bonding network, which preserves both the crystal structure and the highly conductive Pd-derived metallic state under pressure.