Electrons as a Liquid: A Ring Channel and a Magnetic Field ✛

Original: "Hydrodynamic magnetotransport in a GaAs Corbino geometry"
arXiv:2609.10511v1 · 2026-09-09 · CC BY 4.0 · 2 min
In a ring-shaped channel of gallium arsenide, electrons flow like a liquid, and a magnetic field helps measure their viscosity.

A ring-shaped channel of gallium arsenide is like a round swimming pool with no rim: electrons flow in through the inner bank and out through the outer one. In an ultraclean material, they collide with one another more often than with lattice defects, and they start to behave like a liquid. Switch on a magnetic field and it sets this flow swirling, so the resistance of the channel grows. What is more, it grows in proportion to the square of the field, and that growth tells you the viscosity of the electron liquid.

Viscosity is a liquid's resistance to a change in the shape of its flow. The higher the viscosity, the more the flow clings to itself, and the harder it is to set swirling.

The researchers fabricated several rings of different sizes and measured the resistance at different temperatures. It turned out that the coefficient in front of the square of the field grows with the size of the ring and falls with temperature. This is exactly what theory predicts: in a larger ring the liquid has more room to show its viscosity, while heating makes the electrons collide more often and the viscosity drop.

So the ring channel has become a new tool for measuring the viscosity of the electron liquid. Previously this was done mainly with Hall bars, but there the result depended on how the electrons interact with the side walls. In a ring that source of uncertainty disappears, and only the bulk flow remains. Physicists can now test theories of electron hydrodynamics on a cleaner platform.

The relative magnetoresistance in these devices reached $10^4$%, which means a hundredfold change in resistance in a field of just 0.2 T. By comparison, ordinary metals change their resistance by fractions of a percent in such fields.

R(B)-R(0)=\alpha B^2
Resistance grows in proportion to the square of the magnetic field; the coefficient α depends on temperature and radius.
l_G=\sqrt{\nu\tau_{mr}}
The characteristic scale at which viscosity becomes comparable to momentum relaxation; it determines the crossover between hydrodynamic and diffusive regimes.
\tau_{2,ee}^{-1}=A_{ee}\frac{k_B^2}{\hbar E_F}T^2
The contribution of electron-electron collisions to the relaxation of the second harmonic of the distribution function, growing as the square of the temperature.
Concepts
magnetoresistance microorganism swimming dynamics alfven wave