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 resistance1-4, higher-than-ballistic conduction5-7, Poiseuille flow in narrow channels8-10 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.

Long-range nontopological edge currents in charge-neutral graphene.

Van der Waals heterostructures display numerous unique electronic properties. Nonlocal measurements, wherein a voltage is measured at contacts placed far away from the expected classical flow of charge carriers, have been widely used in the search for novel transport mechanisms, including dissipationless spin and valley transport1-9, topological charge-neutral currents10-12, hydrodynamic flows13 and helical edge modes14-16. Monolayer1-5,10,15-19, bilayer9,11,14,20 and few-layer21 graphene, transition-metal dichalcogenides6,7 and moiré superlattices8,10,12 have been found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated3,11,17,22-24. Graphene, in particular, exhibits giant nonlocality at charge neutrality1,15-19, a striking behaviour that has attracted competing explanations. Using a superconducting quantum interference device on a tip (SQUID-on-tip) for nanoscale thermal and scanning gate imaging25, here we demonstrate that the commonly occurring charge accumulation at graphene edges23,26-31 leads to giant nonlocality, producing narrow conductive channels that support long-range currents. Unexpectedly, although the edge conductance has little effect on the current flow in zero magnetic field, it leads to field-induced decoupling between edge and bulk transport at moderate fields. The resulting giant nonlocality at charge neutrality and away from it produces exotic flow patterns that are sensitive to edge disorder, in which charges can flow against the global electric field. The observed one-dimensional edge transport is generic and nontopological and is expected to support nonlocal transport in many electronic systems, offering insight into the numerous controversies and linking them to long-range guided electronic states at system edges.

Imaging work and dissipation in the quantum Hall state in graphene.

Topology is a powerful recent concept asserting that quantum states could be globally protected against local perturbations1,2. Dissipationless topologically protected states are therefore of major fundamental interest as well as of practical importance in metrology and quantum information technology. Although topological protection can be robust theoretically, in realistic devices it is often susceptible to various dissipative mechanisms, which are difficult to study directly because of their microscopic origins. Here we use scanning nanothermometry3 to visualize and investigate the microscopic mechanisms that undermine dissipationless transport in the quantum Hall state in graphene. Simultaneous nanoscale thermal and scanning gate microscopy shows that the dissipation is governed by crosstalk between counterpropagating pairs of downstream and upstream channels that appear at graphene boundaries as a result of edge reconstruction. Instead of local Joule heating, however, the dissipation mechanism comprises two distinct and spatially separated processes. The work-generating process that we image directly, which involves elastic tunnelling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. By contrast, the heat and entropy generation process-which we visualize independently-occurs nonlocally upon resonant inelastic scattering from single atomic defects at graphene edges, and does not affect transport. Our findings provide an insight into the mechanisms that conceal the true topological protection, and suggest routes towards engineering more robust quantum states for device applications.

Publisher Correction: Imaging work and dissipation in the quantum Hall state in graphene.

An Amendment to this paper has been published and can be accessed via a link at the top of the paper.

Demonstration and imaging of cryogenic magneto-thermoelectric cooling in a van der Waals semimetal.

Attaining viable thermoelectric cooling at cryogenic temperatures is of considerable fundamental and technological interest for electronics and quantum materials applications. In-device temperature control can provide more efficient and precise thermal environment management compared with conventional global cooling. The application of a current and perpendicular magnetic field gives rise to cooling by generating electron-hole pairs on one side of the sample and to heating due to their recombination on the opposite side, which is known as the Ettingshausen effect. Here we develop nanoscale cryogenic imaging of the magneto-thermoelectric effect and demonstrate absolute cooling and an Ettingshausen effect in exfoliated WTe2 Weyl semimetal flakes at liquid He temperatures. In contrast to bulk materials, the cooling is non-monotonic with respect to the magnetic field and device size. Our model of magneto-thermoelectricity in mesoscopic semimetal devices shows that the cooling efficiency and the induced temperature profiles are governed by the interplay between sample geometry, electron-hole recombination length, magnetic field, and flake and substrate heat conductivities. The observations open the way for the direct integration of microscopic thermoelectric cooling and for temperature landscape engineering in van der Waals devices.