[Paper Review] Non-local electrodynamics in ultra-pure PdCoO$_{2}$

Graham Baker, Timothy Branch+12 more|arXiv (Cornell University)|Apr 29, 2022

Surface and Thin Film Phenomena4 citations

TL;DR

This study employs broadband microwave spectroscopy to investigate non-local electrodynamics in ultra-pure PdCoO₂, revealing that its highly anisotropic, facetted hexagonal Fermi surface leads to unconventional frequency-dependent surface resistance. The results favor ballistic electron transport over viscous flow and demonstrate that Fermi surface geometry can mimic diffusive transport signatures, challenging conventional diagnostics of non-local regimes.

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 PdCoO$_{2}$. This permits a particularly elegant symmetry-based diagnostic for non-local electrodynamics, with the result favouring ballistic over strictly hydrodynamic flow. Furthermore, it uncovers a new effect for ballistic electron flow, owing to the highly facetted shape of the hexagonal Fermi surface. We combine our extensive dataset with an analysis of the Boltzmann equation to characterize the non-local regime in PdCoO$_{2}$. 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 ultra-high conductivity materials.

Motivation & Objective

• To distinguish between ballistic and viscous electron transport in ultra-high-purity materials using frequency-dependent measurements.
• To investigate how Fermi surface geometry and symmetry influence non-local electrodynamics in the microwave regime.
• To develop and validate a broadband microwave spectroscopy technique capable of probing AC electrodynamics beyond the DC limit.
• To test the predictive power of Boltzmann transport theory with realistic Fermi surface parameterizations in non-local transport regimes.
• To identify experimental signatures that can unambiguously differentiate between diffusive, viscous, and ballistic transport in anisotropic materials.

Proposed method

• Utilization of a bespoke broadband bolometric microwave spectrometer to measure surface resistance across 0.6–20 GHz in ultra-pure PdCoO₂, Sr₂RuO₄, and Sn.
• Employment of three distinct sample geometries with identical diffusive predictions to isolate non-local effects via symmetry-based diagnostics.
• Application of a generalized Boltzmann transport theory incorporating momentum-conserving and momentum-relaxing scattering, with realistic Fermi surface parameterizations.
• Analysis of frequency-dependent surface resistance to identify power-law deviations from classical and anomalous skin effect predictions.
• Use of hexagonal symmetry in PdCoO₂ to probe orientation-dependent transport behavior and test Pippard theory breakdown.
• Comparison of experimental data with theoretical predictions for ballistic, viscous, and diffusive regimes to determine the dominant transport mechanism.

Experimental results

Research questions

• RQ1 Can broadband microwave spectroscopy resolve the nature of non-local transport in ultra-pure metals when DC measurements are ambiguous?
• RQ2 How does the anisotropic, facetted Fermi surface of PdCoO₂ alter the frequency dependence of surface resistance compared to isotropic models?
• RQ3 To what extent can Fermi surface geometry mimic diffusive transport signatures, such as ω¹/² frequency dependence, in ballistic regimes?
• RQ4 Does momentum-conserving scattering dominate over momentum-relaxing scattering in determining the non-local response in ultra-pure PdCoO₂?
• RQ5 Can the breakdown of Pippard theory in PdCoO₂ be attributed to the interplay between Fermi surface geometry and AC frequency?

Key findings

• The surface resistance in ultra-pure PdCoO₂ deviates significantly from classical and anomalous skin effect predictions, indicating non-local electrodynamics beyond standard models.
• The observed frequency dependence in one crystal orientation follows ω²/³, consistent with ballistic transport, while in another it follows ω¹/², typically associated with diffusive dynamics.
• The Fermi surface's hexagonal, facetted structure is identified as the key factor causing the breakdown of Pippard theory and altering power-law scaling.
• The data strongly favor a ballistic-dominated regime over viscous flow, despite the presence of momentum-conserving scattering.
• The Boltzmann transport model with realistic Fermi surface parameterization successfully reproduces the experimental frequency dependence, validating its use in non-local transport analysis.
• This work represents the first experimental observation of the anomalous skin effect outside elemental metals, extending its relevance to complex oxide materials.