Quantum-critical conductivity of the Dirac fluid in graphene

Graphene near charge neutrality is expected to behave like a quantum-critical, relativistic plasma-the ``Dirac fluid''-in which massless electrons and holes rapidly collide at a rate proportional to temperature. We measure the frequency-dependent optical conductivity of clean micron-scale graphene encapsulated in hexagonal Boron Nitride at electron temperatures between 77 and 300 K using on-chip terahertz spectroscopy. At charge neutrality, we observe the quantum-critical scattering rate characteristic of the Dirac fluid. At higher doping, we uncover two distinct current-carrying modes with zero and nonzero total momenta, a manifestation of relativistic hydrodynamics. Our work reveals the quantum criticality and unusual dynamic excitations near charge neutrality in graphene.