Abstract: Electric and thermal transport in electronic systems has long been described in terms of a single-particle picture, which emphasizes the role of collisions between electrons and impurities or phonons, with electron-electron interactions playing a secondary role.
It is only in the past two decades that advances in the fabrication of ultra-clean samples have refocused the interest on collective hydrodynamic transport — a transport régime which is controlled by the nearly conserved quantities: number, momentum, and energy, and by electron-electron interactions.
In this talk, I review some of the recent theoretical and experimental progress in our understanding of electronic hydrodynamics in graphene-based materials. I focus on thermal transport and its relation to electric transport, epitomized by the Wiedemann-Franz law, which, in its conventional form, predicts a universal ratio between electric and thermal resistivities. Significant deviations from this prediction are found in single- and double-layer graphene, both in the doped case, where the Wiedemann-Franz ratio is reduced, and in the undoped case, where it is greatly enhanced. In the latter case, an interesting scenario emerges, in which a small amount of disorder helps to expose an underlying singularity of the transport coefficients: vanishing thermal resistivity, finite electric resistivity, and diverging Wiedemann-Franz ratio and Seebeck coefficient.