Hydrodynamics of the electronic Fermi liquid: a pedagogical overview (2504.01249v1)

Abstract: For over a hundred years, electron transport in conductive materials has been primarily described by the Drude model, which assumes that current flow is impeded primarily by momentum-relaxing collisions between electrons and extrinsic objects such as impurities or phonons. In the past decade, however, experiments have increasingly realized ultra-high quality electronic materials that demonstrate a qualitatively distinct method of charge transport called hydrodynamic flow. Hydrodynamic flow occurs when electrons collide much more frequently with each other than with anything else, and in this limit the electric current has long-wavelength collective behavior analogous to that of a classical fluid. While electron hydrodynamics has long been postulated theoretically for solid-state systems, the plethora of recent experimental realizations has reinvigorated the field. Here, we review recent theoretical and experimental progress in understanding hydrodynamic electrons using the (hydrodynamic) Fermi liquid as our prototypical example.

Hydrodynamics of the Electronic Fermi Liquid: An Expert Overview

The paper "Hydrodynamics of the electronic Fermi liquid: a pedagogical overview" by Aaron Hui and Brian Skinner provides an insightful review of the current understanding of hydrodynamic transport in electronic systems, particularly focusing on the context of Fermi liquids. Electron hydrodynamics, distinct from the classical Drude model, becomes relevant when electron-electron interactions dominate over momentum relaxation processes due to impurities or phonons. This results in collective flow behaviors akin to classical fluids, which are increasingly observed in ultra-high purity materials.

Fundamental Framework and Regimes

The authors distinguish between the traditional Drude model, ballistic transport, and the hydrodynamic regime. In the hydrodynamic regime, hydrodynamics becomes a universal framework for explaining transport behavior by focusing on conserved quantities like charge and momentum over long wavelengths. The paper elucidates how the hydrodynamic framework can be systematically applied to understand electron flow in Fermi liquids, emphasizing the continuity and constitutive equations that guide this regime. This involves solving the Navier-Stokes-Ohm equations, where the Gurzhi length $\lambda$ describes the scale of hydrodynamic behavior relative to the system size.

Specific Phenomena

Several phenomena are associated with hydrodynamic electron systems:

• Flow Profiles and Vorticity: The paper discusses flow profiles, such as Poiseuille flow, observed in rectangular channels and the potential for whirlpools or vortices formed under certain conditions. These features are distinct signatures of nonlocal transport behavior facilitated by viscosity.
• Hydrodynamic Resistance: The resistance in this regime deviates from typical ohmic behavior, exhibiting non-trivial scaling with respect to temperature and geometry. The Gurzhi effect, where resistance can decrease with increasing temperature due to reducing viscosity, is particularly noteworthy.
• Viscosity and Superballistic Transport: Viscosity plays a crucial role in defining hydrodynamic flows and can be computed from microscopic theories. Moreover, electron-electron interactions can lead to superballistic transport, where conductance exceeds classical ballistic limits, observable in constriction geometries.
• Corbino Geometry and Paradoxes: The Corbino geometry presents unique challenges, such as the Corbino paradox, where hydrodynamic analyses reveal contact voltage drops and zero bulk electric fields despite current flow.
• Thermal and Thermoelectric Transport: Unlike traditional systems, hydrodynamic systems feature significant violations of the Wiedemann-Franz law, indicative of decoupled electrical and thermal transport timescales. Electron-hole plasmas, exemplified in monolayer graphene, further diversify these transport properties, leading to enhanced thermal conductivity at charge neutrality.
• Role of Smooth Potentials and Current Noise: Current noise, interpreted through shot and Johnson-Nyquist mechanisms, has implications for sensor applications and thermometry. Hydrodynamic flow in smooth disorder potentials, as described, contests simplifying assumptions generally held in transport analysis.

Advanced Topics and Future Prospects

The paper not only reviews known phenomena but also explores advanced topics like nonlinear dynamics and the implications of broken symmetries on viscosity. The pursuit of experimental signatures and applications in systems like monolayer graphene are poised to further uncover the nuances of hydrodynamic transport.

Conclusion

This comprehensive overview emphasizes the theoretical and experimental intricacies of electron hydrodynamics within Fermi liquids. By structuring a pedagogical narrative, the paper serves as a critical resource for experienced researchers, offering perspectives on the intricate blend of quantum mechanics and fluid dynamics that defines the behavior of electrons in high-quality materials. The implications stretch beyond fundamental understanding, bearing potential for technological applications in sensor design and quantum criticality investigations. This work not only revisits but significantly enriches the discourse on electron transport, offering fertile ground for future exploration in condensed matter physics and materials science.