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The outstanding charge transport properties of graphene enable numerous electronic applications of this remarkable material, many of which are expected to operate at ultrahigh speeds. In the regime of ultrafast, sub-picosecond electric fields, however, the very high conduction properties of graphene are not necessarily preserved, with the physical picture explaining this behaviour remaining unclear. Here we show that in graphene, the charge transport on an ultrafast timescale is determined by a simple thermodynamic balance maintained within the graphene electronic system acting as a thermalized electron gas. The energy of ultrafast electric fields applied to graphene is converted into the thermal energy of its entire charge carrier population, near-instantaneously raising the electronic temperature. The dynamic interplay between heating and cooling of the electron gas ultimately defines the ultrafast conductivity of graphene, which in a highly nonlinear manner depends on the dynamics and the strength of the applied electric fields.

Thermodynamic picture of ultrafast charge transport in graphene