Evidence for hydrodynamic electron flow in PdCoO$_2$

TL;DR

This paper provides experimental evidence that electron flow in ultra-pure PdCoO₂ exhibits hydrodynamic behavior, with viscosity significantly influencing electrical resistance, challenging conventional understanding of electron transport in solids.

Contribution

The study demonstrates that electron viscosity can dominate resistance in certain materials, supported by experimental data and theoretical comparison in PdCoO₂.

Findings

Electron flow in PdCoO₂ shows hydrodynamic characteristics.

Electronic viscosity in PdCoO₂ is comparable to water at room temperature.

Viscous effects significantly contribute to resistance in ultra-pure metals.

Abstract

Electron transport is conventionally determined by the momentum-relaxing scattering of electrons by the host solid and its excitations. The electrical resistance is set by geometrical factors and the resistivity, which is a microscopic property of the solid. Hydrodynamic fluid flow through channels, in contrast, is determined by geometrical factors, boundary scattering and the viscosity of the fluid, which is governed by momentum-conserving internal collisions. A long-standing question in the physics of solids, brought into focus by the advent of new calculational techniques, has been whether the viscosity of the electron fluid plays an observable role in determining the resistance. At first sight this seems unlikely, because in almost all known materials the rate of momentum-relaxing collisions dominates that of the momentum-conserving ones that give the viscous term. Here, we show this is not always the case. We report experimental evidence that the resistance of restricted channels of the ultra-pure two-dimensional metal PdCoO$_2$ has a large viscous contribution. Comparison with theory allows an estimate of the electronic viscosity in the range between $6\times 10^{-3}$~kg(ms)$^{-1}$ and $3\times 10^{-4}$~kg(ms)$^{-1}$, which brackets that of water at room temperature.