Nonlocal Electrodynamics in Ultrapure PdCoO_{2}

Abstract

The motion of electrons in the vast majority of conductors is diffusive, obeying Ohm’s law. However, the recent discovery and growth of high-purity materials with extremely long electronic mean free paths has sparked interest in non-Ohmic alternatives, including viscous and ballistic flow. Although non-Ohmic transport regimes have been discovered across a range of materials—including two-dimensional electron gases, graphene, topological semimetals, and the delafossite metals—determining their nature has proved to be challenging. Here, we report on a new approach to the problem, employing broadband microwave spectroscopy of the delafossite metal PdCoO_{2} in three distinct sample geometries that would be identical for diffusive transport. The observed differences, which go as far as differing power laws, take advantage of the hexagonal symmetry of the conducting Pd planes of PdCoO_{2}. This permits a particularly elegant symmetry-based diagnostic for nonlocal electrodynamics, with the result favoring predominantly ballistic over strictly hydrodynamic flow. Furthermore, it uncovers a new effect for ballistic electron flow, owing to the highly faceted shape of the hexagonal Fermi surface. We combine our extensive data set with an analysis of the Boltzmann equation to characterize the nonlocal regime in PdCoO_{2}, and we include out-of-plane impurity scattering as a source of apparent momentum-conserving scattering at low temperatures. More broadly, our results highlight the potential of broadband microwave spectroscopy to play a central role in investigating exotic transport regimes in the new generation of ultrahigh-conductivity materials.