Viscochiral Transport: Chiral Selection of Hydrodynamic Vortices by Berry Curvature

In the world of electricity, we usually think of electrons as tiny, independent particles bouncing off obstacles, much like raindrops hitting a windshield. This is the standard way current flows in most wires, a behavior governed by simple resistance. However, under very specific conditions—such as in ultra-clean materials at extremely low temperatures—electrons can stop acting like individual billiard balls and start behaving like a thick, sticky fluid. In this rare state, known as the hydrodynamic regime, the electrons collide with each other far more often than they hit impurities. This collective behavior allows them to swirl and spin, creating complex flow patterns that look more like water moving through a pipe than electricity moving through a wire. Scientists have recently begun to visualize these swirling currents, but a new question has emerged: what happens when this electron fluid is subjected to a force that breaks the usual symmetry of time, a property called time-reversal symmetry?

A team of researchers at the Massachusetts Institute of Technology has predicted a new state of transport where this electron fluid can be steered to favor one type of spin over another, effectively choosing which way the fluid swirls. They call this the "viscochiral" regime. Their work suggests that by creating a specific kind of imbalance in the material's internal geometry, they can amplify a swirling vortex in one part of a device while completely suppressing a similar swirl in another. This discovery relies on a concept called Hall viscosity, a property that arises when the flow of electrons is influenced by the material's internal structure, specifically a geometric feature known as Berry curvature. While a uniform version of this property does nothing to change the flow of an incompressible fluid, the researchers found that if this property changes from one side of the device to the other, its gradient acts like a directional force. This force can push the fluid's rotation in a specific direction, breaking the natural symmetry of the system.

To test this idea, the researchers modeled a device made of bilayer graphene, a material consisting of two stacked sheets of carbon atoms. They imagined a setup with a central channel feeding into two side chambers, a geometry that naturally encourages the formation of swirling eddies, or vortices, in both chambers. In a standard electron fluid, or one where the internal geometric properties are the same everywhere, these two chambers would host a pair of mirror-image vortices spinning in opposite directions. The flow would be perfectly balanced. However, the team simulated what would happen if the source and the drain of the device were tuned to have opposite magnetic properties, creating a sharp boundary where the internal geometry of the material changes abruptly. In this scenario, the gradient of the Hall viscosity acts as a selector. It does not simply speed up the flow; it actively transfers the strength of the swirl from one chamber to the other.

The results of their simulations reveal a dramatic shift in behavior. As the difference in the internal geometry increases, the vortex in one chamber grows stronger and more energetic, while the vortex in the other chamber weakens until it disappears entirely. The system transforms from a state of two balanced swirls into an asymmetric state with a single, dominant vortex. This transition is not a gradual fading but a distinct switch between two regimes of transport. The researchers identified a specific ratio between the strength of this geometric imbalance and the fluid's internal stickiness that determines when this switch occurs. They found that if the material is already close to losing its fluid-like behavior due to friction with impurities, this geometric imbalance can trigger the single-vortex state with a much smaller push than expected. This creates a "tongue" of stability in their phase diagram, a region where the effect is surprisingly easy to achieve even with modest changes in the material's properties.

The study also clarifies what does not happen in this process. The researchers explicitly ruled out the idea that a uniform, unchanging version of this geometric property could alter the flow pattern. If the internal geometry is the same everywhere, the fluid flows exactly as it would without this property, maintaining its mirror symmetry. The effect is entirely dependent on the change, or gradient, of the property across the device. Furthermore, the mechanism is not tied to the specific shape of the chambers or the microscopic details of the graphene; it is a generic feature of any recirculating flow where such a gradient exists. The researchers are confident in these findings because they are derived from fundamental equations of fluid dynamics adapted for electrons, and they point to a clear, measurable signature: the disappearance of one vortex and the amplification of the other.

Looking toward the real world, the authors suggest that this phenomenon is within reach of current experimental technology. They propose that by using a bilayer graphene device and applying magnetic fields in opposite directions at the source and the drain, scientists could create the necessary valley-polarized phases to generate the required gradient. In such an experiment, the flow profiles could be mapped using sensitive magnetic sensors, revealing the stark difference between the two chambers. The researchers estimate that with realistic material parameters, the conditions needed to observe this effect fall squarely within the range of what can be achieved in a laboratory. This work opens a new door for controlling electron flow, not by changing the voltage or the shape of the wire, but by tuning the internal geometric landscape of the material itself, offering a new way to manipulate the collective behavior of electrons in future electronic devices.