Imaging ballistic and viscous electron flow in dual-gated rhombohedral graphene (Part II)

Rhombohedral multilayer graphene hosts a variety of correlated electronic phases, including isospin Stoner ferromagnetism and chiral superconductivity, enabled by the displacement-field tunability of its band structure. A previous transport study has reported a resistivity minimum above the Curie temperature of symmetry-broken phases in this system, associated with scattering from fluctuating magnetic moments, suggesting that electron-electron interactions and magnetic fluctuations strongly influence charge transport [1].

Here, we use nanoSQUID-on-tip (nSOT) microscopy to directly image current flow in dual-gated rhombohedral multilayer graphene patterned into a “dumbbell” geometry. We track the evolution of vortices in the current flow across carrier density, displacement field, and applied current, and identify ballistic, viscous (hydrodynamic), and diffusive (Ohmic) transport regimes through quantitative comparison with numerical simulations. At the base temperature of 1.6K and low bias currents, ballistic vortices dominate at high carrier densities, with a crossover to viscous flow upon entering the fluctuating moment phase, where transport anomalies were observed. Increasing electron temperature expands the viscous regime at the expense of the ballistic regime while also accentuating nonlinear effects. Moreover, intrusion of central laminar flow leads to strongly deformed vortices near charge neutrality, a hallmark of the viscous-to-diffusive crossover.

Our results directly link microscopic current flow to correlated transport in rhombohedral multilayer graphene, bridging the ballistic, hydrodynamic, and diffusive regimes, and highlighting the role of fluctuating spin moments in electron scattering.

[1] Holleis, L. et al. Fluctuating magnetism and Pomeranchuk effect in multilayer graphene. Nature 640, 355–360 (2025).