Electron hydrodynamics in ultra-clean conductors: from Dirac fluids in graphene to viscous metals

Abstract

This work examines the emerging field of electron hydrodynamics in ultra-clean conductors, where charge carriers behave collectively as a viscous fluid rather than as independent quasiparticles. The objective is to provide a unified perspective that connects theoretical frameworks with key experimental realizations in graphene, delafossite metals and topological semimetals. To this end, we performed a structured literature search across major databases and preprint servers, applied explicit inclusion and exclusion criteria to identify genuinely hydrodynamic studies, and carried out a comparative, narrative analysis of transport, thermal and imaging experiments. The collected evidence shows that hydrodynamic transport arises when electron–electron collisions dominate over momentum-relaxing processes and when device dimensions are comparable to characteristic scattering lengths. In this regime, experiments reveal geometry-dependent resistivity, negative nonlocal signals, super-ballistic conductance, strong violations of the Wiedemann–Franz law and, in some cases, Hall viscosity. Graphene provides the clearest realization of a relativistic Dirac fluid, while PdCoO₂ and WP₂ demonstrate that viscous electron flow also occurs in anisotropic and multi-band metals. This work highlights that boundaries, disorder and Fermi-surface geometry critically shape hydrodynamic signatures and must be incorporated into any quantitative interpretation. It identifies open issues concerning the roles of phonons and Umklapp processes, the reliable extraction of viscosity, and the extension of hydrodynamics to more complex correlated and topological phases. Finally, it outlines priorities for future “benchmark” experiments that combine nonlocal transport, thermal measurements and real-space imaging within the same devices.