The delafossite metal PdCoO₂ has been shown to exhibit an array of exotic DC transport phenomena due to its exceptionally long mean free path and nearly hexagonal Fermi surface [1]. Here we present AC microwave spectroscopy measurements in two geometries for which, from the symmetry of the crystallographic lattice, one would conventionally expect the same result. Instead, the two measurements differ strongly in magnitude and frequency dependence. This is evidence for non-local electrodynamics, in which the mean free path is longer than the electromagnetic penetration depth and the conductivity is wavevector-dependent. While the theoretical description of non-local electrodynamics has historically been rooted in ellipsoidal Fermi surfaces [2], here we discuss how the strongly-faceted Fermi surface of PdCoO₂ results in novel phenomenology.

[1] A.P. Mackenzie, Rep. Prog. Phys. 80 032501 (2017)
[2] G.E.H. Reuter and E.H. Sondheimer, Proc. R. Soc. Lond. 195, 336 (1948)