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 collide at a rapid rate. We used on-chip terahertz spectroscopy to measure the frequency-dependent optical conductivity of clean, micrometer-scale graphene at electron temperatures between 77 and 300 kelvin. At charge neutrality, we observed the quantum-critical scattering rate characteristic of the Dirac fluid. At higher doping, we detected 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.