Dissipative and Hall Viscosity of a Disordered 2D Electron Gas

Anti-Poiseuille flow by spin Hall effect

Hydrodynamics is known to emerge in electron flow when the electron-electron interaction dominates over the other momentum-nonconserving scatterings. The hydrodynamic equation that describes the electric current includes viscosity, extending beyond the Ohmic flow. The laminar flow of such a viscous electron fluid in a sample with finite width is referred to as the Poiseuille flow, where the flow velocity is maximum at the center and decreases towards the edges of the sample. In this paper, we show a unique viscous electron fluid arising in electron systems exhibiting the spin Hall effect (spin Hall systems), where the charge and spin currents are coupled. Such a viscous electron fluid emerges even in noninteracting electron systems, and the current density exhibits a minimum at the center of a flow and a maximum at the edges, i.e. an anti-Poiseuille flow realizing. We also find that the spin accumulation by the spin Hall effect is connected to the electric current vorticity in two-dimensional (2D) spin Hall systems. Furthermore, we propose a novel guiding principle to manipulate topological magnetic textures from the hydrodynamic viewpoint. By solving the hydrodynamic equation in a 2D spin Hall system with a cavity and employing micromagnetic simulations for an attached chiral magnetic insulator, we demonstrate that spin accumulation near the cavity's boundary leads to creating a magnetic skyrmion. Our research illuminates new aspects of electron hydrodynamics and spintronics, contributing significant insights to the fields.

Direct observation of vortices in an electron fluid

Vortices are the hallmarks of hydrodynamic flow. Strongly interacting electrons in ultrapure conductors can display signatures of hydrodynamic behaviour, including negative non-local resistance^1-4, higher-than-ballistic conduction^5-7, Poiseuille flow in narrow channels^8-10 and violation of the Wiedemann-Franz law¹¹. Here we provide a visualization of whirlpools in an electron fluid. By using a nanoscale scanning superconducting quantum interference device on a tip¹², we image the current distribution in a circular chamber connected through a small aperture to a current-carrying strip in the high-purity type II Weyl semimetal WTe₂. In this geometry, the Gurzhi momentum diffusion length and the size of the aperture determine the vortex stability phase diagram. We find that vortices are present for only small apertures, whereas the flow is laminar (non-vortical) for larger apertures. Near the vortical-to-laminar transition, we observe the single vortex in the chamber splitting into two vortices; this behaviour is expected only in the hydrodynamic regime and is not anticipated for ballistic transport. These findings suggest a new mechanism of hydrodynamic flow in thin pure crystals such that the spatial diffusion of electron momenta is enabled by small-angle scattering at the surfaces instead of the routinely invoked electron-electron scattering, which becomes extremely weak at low temperatures. This surface-induced para-hydrodynamics, which mimics many aspects of conventional hydrodynamics including vortices, opens new possibilities for exploring and using electron fluidics in high-mobility electron systems.

Viscometry of Electron Fluids from Symmetry

When electrons flow as a viscous fluid in anisotropic metals, the reduced symmetry can lead to exotic viscosity tensors with many additional, nonstandard components. We present a viscometry technique that can, in principle, measure the multiple dissipative viscosities allowed in isotropic and anisotropic fluids alike. By applying representation theory to exploit the intrinsic symmetry of the fluid, our viscometry is also exceptionally robust to both boundary complications and ballistic effects. We present the technique via the illustrative example of dihedral symmetry, relevant in this context as the point symmetry of 2D crystals. Finally, we propose a present-day realizable experiment for detecting, in a metal, a novel hydrodynamic phenomenon: the presence of rotational dissipation in an otherwise isotropic fluid.

Quantizing viscous transport in bilayer graphene

The momentum transport in ultraclean bilayer graphene is characterized by the viscous transport. In quantizing magnetic field the momentum current passes through the guiding center of the cyclotron orbit. In this study we derive the formula of the quantized Hall viscosity for bilayer graphene. This can be detected in the non-local magnetoresistivity measurements that varies with the quantized step. For weak magnetic field the Landau levels start overlapping and lead to the Shubnikov-de-Haas oscillations, superimposed on the classical formulae, reference Steinberg (1958Phys. Rev.1091486). These oscillations are present in the longitudinal and Hall viscosities.