Unraveling the unusually high electrical conductivity of the delafossite metal PdCoO$_2$

The prototypical delafossite metal PdCoO$_2$ has been the subject of intense interest for hosting exotic transport properties. Using first-principles transport calculations and theoretical modeling, we reveal that the high electrical conductivity of PdCoO$_2$ at room temperature originates from the contributions of both high Fermi velocities, enabled by Pd $4d_{z^2}-5s$ hybridization, and exceptionally weak electron-phonon coupling, which leads to a coupling strength ($\lambda=0.057$) that is nearly an order of magnitude smaller than those of common metals. The abnormally weak electron-phonon coupling in PdCoO$_2$ results from a low electronic density of states at the Fermi level, as well as the large and strongly facetted Fermi surface with suppressed Umklapp electron-phonon matrix elements. We anticipate that our work will inform the design of unconventional metals with superior transport properties.