Universality in quantum critical flow of charge and heat in ultraclean graphene

Abstract

Close to the Dirac point, graphene is expected to exist in a quantum critical Dirac fluid state, where the flow of both charge and heat can be described with a characteristic d.c. electrical conductivity and thermodynamic variables such as entropy and enthalpy densities. Although the fluid-like viscous flow of charge has been reported in state-of-the-art graphene devices, the value of conductivity, predicted to be quantized and determined only by the universality class of the critical point, has not been established experimentally so far. Here we have discerned the quantum critical universality in graphene transport by combining the electrical and thermal conductivities in very high-quality devices close to the Dirac point. We find that they are inversely related, as expected from relativistic hydrodynamics, and the characteristic conductivity converges to a quantized value. We also observe a giant violation of the Wiedemann–Franz law, where the Lorentz number exceeds the semiclassical value by more than 200 times close to the Dirac point at low temperatures. At high temperatures, the effective dynamic viscosity to entropy density ratio close to the Dirac point in the cleanest devices approaches that of a minimally viscous quantum fluid within a factor of four. Critical behaviour is expected in graphene when the carrier density is tuned to the Dirac point. Now, universality associated with the critical point is observed in electronic and thermal transport.