Superballistic Paradox in Electron Fluids: Relevance of Tomographic Transport

Electron hydrodynamics encompasses the exotic fluidlike behavior of electrons in two-dimensional materials such as graphene. It accounts for superballistic conduction, also known as the Gurzhi effect, where increasing temperature reduces the electrical resistance. In analogy with conventional fluids, the Gurzhi effect is only expected in the hydrodynamic regime, with the decrease in the resistance occurring at intermediate temperatures. Nonetheless, experiments on electron fluids consistently show that superballistic conduction starts at close-to-zero temperature. To address this paradox, we study hydrodynamic flow, and we find that replacing the conventional dynamics with tomographic dynamics gives rise to an accurate low-temperature description. The latter strengthens superballistic conduction, with potential applications in low-dissipation devices, and explains its differences with the Molenkamp effect and conventional fluid dynamics. Our study reveals that the superballistic paradox is resolved by considering the peculiarities of electron-electron collisions at the Fermi surface.