Evidence for hydrodynamic electron flow in PdCoO$_2$ (1509.05691v2)

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.

• The paper demonstrates that electron hydrodynamics in PdCoO₂ leads to a quadratic resistivity scaling with channel width due to momentum-conserving interactions.
• The paper employs precise crystal growth, FIB microfabrication, and SEM verification to accurately measure channel dimensions and determine a momentum-relaxing mean free path of ~18.5 μm.
• The paper integrates a semiclassical Boltzmann framework to correlate resistivity with electron viscosity, providing key insights for designing future nanoscale electronic devices.

Analysis of Charge Transport Phenomena in PdCoO$_2$: A Study of Electron Hydrodynamics

This paper presents a comprehensive paper focused on the investigation of charge transport phenomena in PdCoO$_2$, specifically examining the behavior of electron flow in two-dimensional channels under conditions conducive to hydrodynamic transport. The researchers utilize an array of experimental and theoretical techniques to assess momentum-conserving and momentum-relaxing scattering in this high-conductivity material, exploring the intricacies of electron hydrodynamics.

Experimental Methodology and Results

Crystal Growth and Resistivity Calculations

The crystal growth process involved a modified synthesis of PdCoO$_2$ in sealed quartz tubes, followed by a series of characterization methods including x-ray diffraction and transport measurements to assess crystal phase purity and conductivity. Resistivity was computed using a model of homogeneous current flow in parallelepiped geometries. A key observation was that the effective thickness of the sample ($T_e$) involved a correction factor, important for accurately determining the momentum-relaxing mean free path, $\ell_{MR}$, calculated to be approximately 18.5 $\pm$ 1.5 $\mu$m.

Focused Ion Beam Fabrication and Surface Characterization

To explore the influence of channel width on resistivity, micro-channel devices were fabricated using focused ion beam (FIB) techniques. Detailed considerations were given to possible defect generation and sidewall damage during FIB processing. The experimental determination of widths was cross-verified using Scanning Electron Microscope (SEM) images and magnetoresistance measurements, yielding consistent results that underscored high accuracy in width determination and minimal surface damage influences.

Theoretical Insights into Hydrodynamic Electron Flow

Momentum-Scattering Dynamics

The theoretical framework is grounded in a semiclassical approach to electron transport, formulated via the Boltzmann transport equation. The model configures the scattering into two primary categories: momentum-relaxing and momentum-conserving, ignoring electron-phonon interactions. Numerical solutions to derived boundary conditions illustrate how resistivity changes with varying channel width and momentum conservation dynamics.

Viscous Flow in Hydrodynamic Regime

Further analysis interprets the results within a hydrodynamic framework, theoretically describing electrons as a classical fluid characterized by viscosity. In the limit of prominent electron-electron scattering, a quadratic dependence of resistivity on the inverse channel width, akin to viscous contributions, is observed. This articulates an effective exploration of electron hydrodynamics as resistivity varies in response to channel narrowing in PdCoO$_2$.

Implications and Future Directions

The implications of this research lie both in the explicit characterization of electron hydrodynamics in high-purity, low-dimensional metal systems, and in the potential application of these phenomena in designing devices where electron flow mimics those of classical fluids. Practical advances might refine methodologies for fabricating micro-structured electronic materials with controlled resistive properties tailored through understanding of intrinsic hydrodynamic electron behaviors.

Looking forward, this paper sets the stage for further exploration into the effects of temperature variation on momentum-conserving processes, sophisticated modeling to better predict hydrodynamic regimes, and experimental validation of theoretical predictions in other candidate materials. Additionally, these advances in understanding electron-electron interactions and resultant hydrodynamic effects might offer insights into novel electronic transport mechanisms applicable in nanoscale device engineering.