Electrons in a material do not always behave as independent particles. When electron-electron collisions dominate over momentum-relaxing processes, they can move collectively in a fluid-like regime known as hydrodynamic electron transport. Distinguishing this collective behavior from conventional diffusion is important for identifying electron hydrodynamics in low-dimensional materials.
A new kinetic-simulation study published in Thermo-X , "Kinetic simulation of magnetic-field-tuned hydro-dynamic electron transport in a graphene Corbino disk," examines how magnetic fields affect charge and heat transport in a graphene Corbino disk.
The simulations identify three signatures that distinguish hydrodynamic from diffusive electron transport: magnetic-field-induced deflection of charge and heat flux; contrasting temperature responses under electric-field driving; and a reversal of the deflection chirality when the driving force changes from an electric field to a temperature gradient.
Magnetic fields expose collective electron motion
The researchers modeled a homogeneous graphene Corbino disk with inner and outer radii in a 1:5 ratio. Using the Boltzmann transport equation and a dual-relaxation-time Callaway model, they separately represented momentum-conserving (MC) and momentum-relaxing (MR) scattering processes.
This distinction is central to electron hydrodynamics. MC scattering allows electrons to exchange momentum while preserving the total momentum of the electron system, which favors collective motion. MR scattering dissipates momentum and suppresses collective drift, steering transport toward the conventional diffusive regime.
When an electric potential difference and a perpendicular magnetic field were applied in the simulations, the two regimes behaved differently. In the diffusive regime, heat flux remained largely radial, with only a small tangential component. In the hydrodynamic regime, both heat flux and electric current were strongly deflected from the radial direction.
The model attributes this contrast to the collective drift velocity that emerges in the hydrodynamic regime. Under electric-field driving, electrons move inward through the disk and experience a Lorentz force. The resulting tangential component of collective motion cannot be fully compensated by the radial electrostatic field in the bulk, leaving a deflected macroscopic flux.
The simulations further show that the deflection depends on the competition between MC and MR scattering. A larger relative contribution from MC scattering strengthens collective drift and promotes flux deflection, whereas stronger MR scattering suppresses mobility and weakens the magnetic response. At fixed scattering rates, the deflection angle increases with magnetic-field strength.
Heat transport provides an additional signature
Under electric-field driving, the simulated graphene disk showed a substantially larger temperature rise in the hydrodynamic regime than in the diffusive regime, which remained nearly isothermal under the reported conditions.
In the model, this contrast is associated with reduced momentum relaxation and the resulting dissipation pattern in the hydrodynamic regime. Joule heating contributes to the radial temperature distribution, while thermoelectric effects also influence heat flow.
The calculated heat flux contains both a dissipative component associated with the temperature gradient and a thermoelectric component associated with electric current. Under the simulated hydrodynamic conditions, the thermoelectric component dominates, producing heat flow from the cooler outer boundary toward the hotter inner boundary. The authors note that this is a thermoelectric response and does not violate Fourier's law.
By contrast, frequent MR scattering in the diffusive regime relaxes momentum gained from the electric field, suppressing sustained acceleration and leaving a much weaker temperature response.
Changing the driving force reverses the deflection chirality
The researchers also modeled a configuration in which the electric and chemical potentials at the inner and outer boundaries were kept equal while a temperature gradient was imposed.
Under temperature-gradient driving, the direction of heat and charge transport reversed relative to the electric-field-driven case. Heat flux traveled from the hotter inner region toward the cooler outer region, while electric current flowed in the opposite direction.
Again, the simulations showed little heat-flux deflection in the diffusive regime but pronounced deflection in the hydrodynamic regime. Crucially, the chirality of the magnetic-field-induced deflection reversed relative to electric-field driving.
The model explains this reversal through the opposite directions in which the two driving forces shift the electron distribution away from equilibrium. Electric-field driving produces inward collective motion, whereas temperature-gradient driving produces the relevant transport in the opposite direction. The Lorentz force therefore acts in opposite tangential directions.
A theoretical route to identifying electron hydrodynamics
Taken together, the simulations identify three physical distinctions between hydrodynamic and diffusive electron transport in the graphene Corbino geometry.
First, magnetic-field-induced flux deflection is pronounced when MC scattering dominates and suppressed when MR scattering dominates. Second, electric-field driving produces a much larger temperature rise in the hydrodynamic regime. Third, switching the driving mechanism from an electric field to a temperature gradient reverses the chirality of the magnetic-field-induced deflection.
These predictions suggest that thermodynamic quantities—particularly magnetic-field-induced heat-flow deflection—could offer an additional way to distinguish hydrodynamic electron flow from classical diffusive transport.
The authors emphasize that these are kinetic-simulation results. Spatially resolved measurements of heat flux or temperature are considerably more challenging than measurements of electrical current or potential. Future advances in thermal measurement techniques may enable direct tests of the predicted signatures.
