Kinetic theory of the non-local electrodynamic response in anisotropic metals: skin effect in 2D systems

TL;DR

This paper develops a kinetic theory to analyze how anisotropic electronic dispersion in ultra-pure metals affects their non-local electrodynamic response, especially the skin effect, revealing orientation-dependent optical phenomena.

Contribution

It introduces a comprehensive kinetic framework for anisotropic Fermi systems, extending understanding of non-local electrodynamics and skin effect in 2D and 3D materials.

Findings

Qualitative differences in impedance frequency dependence between isotropic and anisotropic systems.

Persistence of anisotropic effects even in complex Fermi surface geometries.

Guidance for experimental detection of orientation-dependent non-local optical responses.

Abstract

The electrodynamic response of ultra-pure materials at low temperatures becomes spatially non-local. This non-locality gives rise to phenomena such as hydrodynamic flow in transport and the anomalous skin effect in optics. In systems characterized by an anisotropic electronic dispersion, the non-local dynamics becomes dependent on the relative orientation of the sample with respect to the applied field, in ways that go beyond the usual, homogeneous response. Such orientational dependence should manifest itself not only in transport experiments, as recently observed, but also in optical spectroscopy. In this paper we develop a kinetic theory for the distribution function and the transverse conductivity of two- and three-dimensional Fermi systems with anisotropic electronic dispersion. By expanding the collision integral into the eigenbasis of a collision operator, we include momentum-relaxing scattering as well as momentum-conserving collisions. We examine the isotropic 2D case as a reference, as well as anisotropic hexagonal and square Fermi-surface shapes. We apply our theory to the quantitative calculation of the skin depth and the surface impedance, in all regimes of skin effect. We find qualitative differences between the frequency dependence of the impedance in isotropic and anisotropic systems. Such differences are shown to persist even for more complex 2D Fermi surfaces, including the ''supercircle'' geometry and an experimental parametrization for PdCoO$_2$, which deviate from an ideal polygonal shape. We study the orientational dependence of skin effect due to Fermi-surface anisotropy, thus providing guidance for the experimental study of non-local optical effects.