A computer model of electronic flow associates a spatial change in Hall viscosity with two vortices behaving differently: one becomes stronger while the other weakens and may be completely suppressed. The calculation frames the Hall-viscosity gradient as a spatially varying Berry-curvature effect. It is a theoretical result from a two-chamber model, not a direct observation from an operating device.
The manuscript is an arXiv version 2 preprint. It asks whether a spatial Hall-viscosity gradient can select vortical patterns in electronic transport, using analytical calculations and numerical flow solutions. The comparisons cover a uniform or absent gradient, different Ohmic momentum-relaxation rates and different inlet flow velocities.
How the model defines a vortex
The modeled system is a two-chamber channel with prescribed flow conditions. Velocity is set to zero at the boundaries, while flow enters through a parabolic inlet profile. Within that geometry, the calculations track whether vortices appear and how their relative strengths change as the Hall-viscosity gradient and other flow parameters are varied.
A vortex is not counted simply because a flow map looks circular. The model requires a circulation-like quantity to rise above a threshold and also requires the flow to exceed a minimum speed. That second condition is intended to reduce numerical-noise artifacts, making the reported vortex count a defined output of the calculation.
The spatial contrast is summarized by the dimensionless control parameter χ = ΔηH/μ. The paper treats uniform odd viscosity as leaving the velocity field of an incompressible flow unchanged. In that formulation, the modeled change in bulk flow is tied to spatial variation in Hall viscosity rather than to a uniform value across the channel.
A phase diagram with a narrow low-gradient region
With the gradient included, the analysis reports amplified vorticity in the left chamber and diminished vorticity in the right. That left-right imbalance corresponds to an asymmetric distribution of vortices, with the two chambers no longer behaving as equivalent recirculating regions. The model therefore connects the spatial Hall-viscosity profile with a selected pattern of electronic flow.
The numerical phase diagram separates the modeled behavior into hydrodynamic, viscochiral and Ohmic regimes. The viscochiral regime is the part of the calculation in which the Hall-viscosity variation is associated with the distinctive vortex pattern. As Ohmic dissipation increases, the model is associated with a transition to potential flow without vortices.
The reported transition values depend strongly on the modeled relaxation conditions. At small Ohmic relaxation, the transition to the viscochiral regime occurs at χc ≈ 2.9. Near the hydrodynamic–Ohmic boundary, the phase extends down to about χ ∼ 0.05, nearly two orders of magnitude below the small-relaxation threshold.
Flow speed was another comparison. At low Ohmic damping, changing the inlet velocity to vary the Reynolds number did not move the modeled regime boundary. The result is limited to that low-momentum-relaxation setting and does not establish the same velocity independence under other relaxation conditions.
A proposed graphene test
The authors then use a stated parameter example for valley-polarized Bernal bilayer graphene to examine whether the modeled regime could have a possible experimental platform. Their estimate gives χ ∼ 0.33 and places the example in the viscochiral-tongue region of the phase diagram, where the modeled regime extends to a relatively small Hall-viscosity contrast.
That placement is a model-based estimate, not a demonstrated device result. The paper reports no direct experimental observation of the predicted vortex selection or phase diagram, and it does not establish that the proposed graphene parameters can be achieved in an operating device. Any experimental realization would therefore still need to test the assumptions built into the calculation.
The main evidence comes from the two-chamber geometry. The paper states that the transition is not tied to microscopic device details or the precise chamber shape, but that broader generality is argued within the model rather than demonstrated through direct measurements. The flow is also treated as incompressible throughout, so the reported phase diagram is not a result for every possible electronic-flow condition.
The paper says its code will be made publicly available before publication. Its acknowledgments thank named colleagues for discussions and acknowledge Leonid Levitov for drawing attention to a cited experiment. Funding is not reported in the supplied metadata.
Paper data and sources
Original title: Viscochiral Transport: Chiral Selection of Hydrodynamic Vortices by Berry Curvature
Authors: Archisman Panigrahi, Khachatur Nazaryan
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text