Electron hydrodynamics in anisotropic materials

Abstract

Rotational invariance strongly constrains the viscosity tensor of classical fluids. When this symmetry is broken in anisotropic materials a wide array of novel phenomena become possible. We explore electron fluid behaviors arising from the most general viscosity tensors in two and three dimensions, constrained only thermodynamics and crystal symmetries. We find nontrivial behaviors in both two- and three-dimensional materials, including imprints of the crystal symmetry on the large-scale flow pattern. Breaking time-reversal symmetry introduces a non-dissipative Hall component to the viscosity tensor, and while this vanishes for 3D isotropic systems we show it need not for anisotropic materials. Further, for such systems we find that the electronic fluid stress can couple to the vorticity without breaking time-reversal symmetry. Our work demonstrates the anomalous landscape for electron hydrodynamics in systems beyond graphene, and presents experimental geometries to quantify the effects of electronic viscosity.

Stokes flows in three-dimensional fluids with odd and parity-violating viscosities

“…In general, the fluid can be even less symmetric, for example when the fluid is invariant under a discrete point group. This can happen when multiple external fields that are not parallel to each other are applied, or in electron fluids in crystals (Cook & Lucas 2019;Rao & Bradlyn 2020;Toshio, Takasan & Kawakami 2020;Varnavides et al 2020).…”

“…This can happen when multiple external fields that are not parallel to each other are applied, or in electron fluids in crystals (Cook & Lucas 2019; Rao & Bradlyn 2020; Toshio, Takasan & Kawakami 2020; Varnavides et al. 2020).…”

Anti-Poiseuille flow in neutral graphene

“…The possibility for an electronic system to exhibit the Poiseuille flow in a narrow wire was first pointed out by Gurzhi [19][20][21]. Recently, similar behavior has been a subject of intense theoretical [22][23][24][25][26][27][28][29][30][31][32][33] and experimental [10][11][12][13]22,[34][35][36][37][38][39][40][41][42][43][44] research in the context of electronic transport in high-mobility 2D materials. In contrast to conventional fluids, the electronic flow is affected not only by viscous effects, but also by weak disorder scattering and is characterized by a typical length scale known as the Gurzhi length [26][27][28][29]33]…”

Sondheimer oscillations as a probe of non-ohmic flow in WP2 crystals

“…When momentum-conserving interactions are negligible, ohmic flow at the macro-scale (l MC ≫ d ≫ l MR ) gives way to ballistic transport in clean metals where l MR , l MC ≫ d. Conversely, when momentum-conserving interactions occur over similar or smaller length scales to momentum-relaxing interactions, a third regime of 'hydrodynamic' transport (l MR ≫ d ≫ l MC ) is observable 1,2 . In this regime, the static transport properties of electron fluids can be described by an effective viscosity that captures the momentum diffusion of the system 2,3 . These electron fluids exhibit classical fluid phenomena such as Poiseuille flow, whereby the current flow density is greatly decreased at the conductor boundary.…”

“…These electron fluids exhibit classical fluid phenomena such as Poiseuille flow, whereby the current flow density is greatly decreased at the conductor boundary. Recently, advances in both experimental probes and theoretical descriptions have enabled direct observation of these effects using spatially resolved current density imaging, and have hinted towards the rich landscape of electron hydrodynamics in micro-scale crystals [3][4][5] .…”