Conducting materials typically exhibit either diffusive or ballistic charge transport. However, when electron-electron interactions dominate, a hydrodynamic regime with viscous charge flow emerges (1-13). More stringent conditions eventually yield a
quantum-critical Dirac-fluid regime, where electronic heat can flow more efficiently than charge (14-22). Here we observe heat transport in graphene in the diffusive and hydrodynamic regimes, and report a controllable transition to the Dirac-fluid regime at room temperature, using carrier temperature and carrier density as control knobs. We introduce the technique of spatiotemporal thermoelectric microscopy with femtosecond temporal and nanometre spatial resolution, which allows for tracking electronic heat spreading. In the diffusive regime, we find a thermal diffusivity of $sim$2,000 cm$^2$/s, consistent with charge transport. Remarkably, during the hydrodynamic time window before momentum relaxation, we observe heat spreading corresponding to a giant diffusivity up to 70,000 cm$^2$/Vs, indicative of a Dirac fluid. These results are promising for applications such as nanoscale thermal management.
The ultrafast response of metals to light is governed by intriguing non-equilibrium dynamics involving the interplay of excited electrons and phonons. The coupling between them gives rise to nonlinear diffusion behavior on ultrashort timescales. Here
, we use scanning ultrafast thermo-modulation microscopy to image the spatio-temporal hot-electron diffusion in a thin gold film. By tracking local transient reflectivity with 20 nm and 0.25 ps resolution, we reveal two distinct diffusion regimes, consisting of an initial rapid diffusion during the first few picoseconds after optical excitation, followed by about 100-fold slower diffusion at longer times. We simulate the thermo-optical response of the gold film with a comprehensive three-dimensional model, and identify the two regimes as hot-electron and phonon-limited thermal diffusion, respectively.
