• Accepted Paper

Hydrodynamics of the viscous electron fluid in cadmium

Xiaodong Guo, Xiaokang Li, Benoît Fauqué, Alaska Subedi, Lingxiao Zhao, Zengwei Zhu, and Kamran Behnia

Phys. Rev. Lett. - Accepted 19 August, 2026

DOI: https://doi.org/10.1103/g32f-j6q2

Abstract

Thanks to electron-electron (e-e) collisions conserving momentum, metallic electron fluids are viscous. Yet, this viscosity is rarely detectable in bulk transport. Here, we report on the canonical realization of the Gurzhi effect in an elemental three-dimensional metal: cadmium. Using focused ion beam microstructuring to tune the effective thickness, we detected a low-temperature size-dependent resistivity upturn in a finite window sandwiched between ballistic and diffusive regimes. Within this window, the electrical conductivity displays a simultaneous quadratic dependence on both sample size and temperature— fingerprint of a hydrodynamic flow. This leads us to quantify the amplitude and the temperature dependence of kinematic and dynamic viscosity of the electron fluid. In cadmium, in contrast with graphene and 3He, the rate of momentum-conserving e-e collisions is not set by the main Fermi energy, but by Lilliputian energy scales and inter-valley bottlenecks.

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