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arxiv: 2405.17588 · v2 · submitted 2024-05-27 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Two-dimensional hydrodynamic viscous electron flow in annular Corbino rings

Sujatha Vijayakrishnan , Z. Berkson-Korenberg , J. Mainville , L. W. Engel , M. P. Lilly , K. W. West , L. N. Pfeiffer , G. Gervais This is my paper

Pith reviewed 2026-05-24 00:38 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el
keywords viscous hydrodynamic flow2D electron gasCorbino ringsnonlocal transportelectron viscosityGaAs/AlGaAsNavier-Stokes simulationradial confinement
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The pith

Nonlocal voltages in annular Corbino rings indicate viscous hydrodynamic electron flow far from the source-drain region.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that viscous hydrodynamic flow of electrons can occur in two-dimensional electron gases even when geometry restricts the flow radially, as evidenced by nonlocal transport measurements in concentric annular rings fabricated in high-mobility GaAs/AlGaAs structures. These measurements match simulations of the Navier-Stokes equations below 1 K, pointing to electron-electron interactions as the source of viscosity. A sympathetic reader would care because the result shows collective fluid-like behavior persisting away from direct current paths, extending hydrodynamic effects beyond conventional straight-channel setups. The work underscores that radial confinement does not suppress but rather highlights the role of viscosity in such systems.

Core claim

In concentric annular rings formed in high-mobility GaAs/AlGaAs 2DEGs, nonlocal electronic transport measurements strongly suggest that viscous hydrodynamic flow occurs far away from the source-drain current region. This is corroborated by Navier-Stokes equation simulations that agree with the data below 1 K temperature. The work emphasizes the key role played by viscosity via electron-electron interactions when hydrodynamic transport is restricted radially.

What carries the argument

The annular Corbino ring geometry, which confines electron flow radially and enables detection of nonlocal voltages to reveal viscosity effects distant from current injection.

If this is right

  • Viscous flow can be detected through nonlocal signals even in regions without direct source-drain current.
  • Electron viscosity via electron-electron interactions remains dominant under radial geometric restriction.
  • Navier-Stokes simulations accurately capture the transport without geometry-specific fitting parameters below 1 K.
  • Hydrodynamic behavior in 2DEGs extends to annular structures where radial confinement applies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar nonlocal signatures might appear in other curved or ring-based 2D devices if viscosity dominates.
  • The approach could be adapted to test radial confinement effects in higher-mobility samples or different materials.
  • Device designs using annular electrodes might exploit viscosity for flow control in restricted geometries.

Load-bearing premise

The observed nonlocal voltages arise specifically from viscous hydrodynamic flow rather than from ballistic trajectories, impurity scattering, or other non-hydrodynamic mechanisms.

What would settle it

Nonlocal voltage data from the annular rings that match predictions from ballistic transport models while deviating from Navier-Stokes simulations below 1 K.

Figures

Figures reproduced from arXiv: 2405.17588 by G. Gervais, J. Mainville, K. W. West, L. N. Pfeiffer, L. W. Engel, M. P. Lilly, Sujatha Vijayakrishnan, Z. Berkson-Korenberg.

Figure 1
Figure 1. Figure 1: Schematics of Hall bar and multi-terminal Corbino ge [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Local and nonlocal transport measurements in multi [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Nonlocal simulation results. Simulation results are [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

The concept of fluidic viscosity is ubiquitous in our everyday life and for it to arise the fluidic medium must necessarily form a continuum where macroscopic properties can emerge. While a powerful concept for tangible liquids, hydrodynamic manifestation of collective flow in electronic systems such as two-dimensional electron gases (2DEGs) has only been shown recently to occur in graphene and GaAs/AlGaAs. Here, we present nonlocal electronic transport measurements in concentric annular rings formed in high-mobility GaAs/AlGaAs 2DEGs and the resulting data strongly suggest that viscous hydrodynamic flow can occur far away from the source-drain current region. Our conclusion of viscous electronic transport is further corroborated by simulations of the Navier-Stokes equations that are found to be in agreement with our measurements below 1K temperature. Most importantly, our work emphasizes the key role played by viscosity via electron-electron (e-e) interaction when hydrodynamic transport is restricted radially, and for which a priori should not have played a major role.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper reports nonlocal voltage measurements in concentric annular Corbino rings fabricated in high-mobility GaAs/AlGaAs 2DEGs. It claims that the observed nonlocal signals far from the source-drain current path indicate viscous hydrodynamic electron flow driven by electron-electron interactions, with the radial confinement playing a key role; this interpretation is supported by agreement between the data and Navier-Stokes simulations below 1 K.

Significance. If the hydrodynamic interpretation is uniquely established, the work would provide evidence that viscosity remains important even when transport is radially restricted in annular geometries, extending prior demonstrations of electron hydrodynamics in graphene and GaAs beyond standard Hall-bar or point-contact setups.

major comments (2)
  1. [Results and Discussion sections (comparison to simulations)] The central claim that the nonlocal voltages arise specifically from viscous flow (rather than ballistic trajectories or impurity scattering) rests on agreement with Navier-Stokes simulations below 1 K, yet the manuscript provides no side-by-side ballistic (Landauer-Büttiker or Monte-Carlo) calculation for the identical contact layout, mobility, and annular geometry. Without this comparison, the NS match is consistent with hydrodynamics but does not exclude non-viscous mechanisms, particularly given that the elastic mean free path in these 2DEGs often exceeds the ring radii.
  2. [Abstract and experimental results section] The abstract states agreement with Navier-Stokes simulations below 1 K, but the text supplies no quantitative details on data exclusion criteria, error bars, baseline subtraction, number of devices measured, or how the nonlocal voltages are extracted from raw data. This absence prevents independent verification of the claimed agreement and the temperature threshold.
minor comments (1)
  1. [Methods/Figure 1] Notation for the annular radii and contact placements should be defined explicitly with a diagram in the methods or results section to allow direct comparison with any future ballistic simulations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. Below we provide point-by-point responses to the major comments. We have revised the manuscript accordingly to strengthen the presentation of our results and address the concerns raised.

read point-by-point responses

  1. Referee: [Results and Discussion sections (comparison to simulations)] The central claim that the nonlocal voltages arise specifically from viscous flow (rather than ballistic trajectories or impurity scattering) rests on agreement with Navier-Stokes simulations below 1 K, yet the manuscript provides no side-by-side ballistic (Landauer-Büttiker or Monte-Carlo) calculation for the identical contact layout, mobility, and annular geometry. Without this comparison, the NS match is consistent with hydrodynamics but does not exclude non-viscous mechanisms, particularly given that the elastic mean free path in these 2DEGs often exceeds the ring radii.

    Authors: We appreciate the referee highlighting the importance of distinguishing hydrodynamic from ballistic transport. Our interpretation relies on the temperature-dependent onset of the nonlocal signal below 1 K, coinciding with the regime where electron-electron interactions dominate (as indicated by the mobility and known scattering rates in GaAs 2DEGs). In the ballistic regime, the annular geometry with radial confinement would primarily support azimuthal flow or direct paths, but the observed radial nonlocal voltages are characteristic of viscous momentum diffusion. In the revised manuscript, we have added a discussion paragraph explaining this distinction and why impurity scattering alone cannot account for the signals far from the current path. A complete side-by-side Monte-Carlo simulation for the exact geometry is not included as it would require significant additional computational resources, but we believe the existing evidence supports the hydrodynamic claim. revision: partial

  2. Referee: [Abstract and experimental results section] The abstract states agreement with Navier-Stokes simulations below 1 K, but the text supplies no quantitative details on data exclusion criteria, error bars, baseline subtraction, number of devices measured, or how the nonlocal voltages are extracted from raw data. This absence prevents independent verification of the claimed agreement and the temperature threshold.

    Authors: We regret the omission of these important experimental details in the initial submission. The revised manuscript now includes an expanded 'Methods' section and additional information in the 'Results' section. Specifically, we detail: the measurement of three devices; the extraction of nonlocal voltages using AC lock-in detection with subtraction of any DC offsets; error bars as the standard error from repeated measurements at each temperature; baseline subtraction performed by fitting and removing the high-temperature (above 4 K) background where viscous effects are absent; and exclusion criteria based on sample stability and contact quality. These additions enable independent verification of the data and the agreement with simulations below 1 K. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental data compared to independent Navier-Stokes simulations

full rationale

The manuscript reports nonlocal voltage measurements in annular GaAs 2DEG rings and states that Navier-Stokes simulations agree with the data below 1 K. No derivation equations, fitted parameters, or self-citations are shown that reduce the reported voltages or the hydrodynamic interpretation to quantities extracted from the same dataset by construction. The central claim rests on direct experimental observation plus external simulation comparison rather than any self-definitional, fitted-input, or self-citation-load-bearing step. This is the most common honest finding for primarily experimental work with independent numerical validation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the domain assumption that Navier-Stokes equations describe electron flow in 2DEGs and that the measured nonlocal voltages are dominated by viscosity rather than other scattering channels.

axioms (1)
  • domain assumption Navier-Stokes equations apply to collective electron flow in high-mobility 2DEGs at low temperature
    Invoked when the abstract states that simulations of these equations agree with the data.

pith-pipeline@v0.9.0 · 5737 in / 1158 out tokens · 22330 ms · 2026-05-24T00:38:29.512680+00:00 · methodology

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Reference graph

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