Electronic Poiseuille Flow in Hexagonal Boron Nitride Encapsulated Graphene FETs

In most conductors, diffusive scattering from defects and phonons leads to an Ohmic transport. Charge carriers traveling across the channel suffer many momentum relaxing collisions leading to a constant drift velocity along the direction of the applied electric field. Alternatively, transport is ballistic, when the channel dimensions are the smallest length scale in the system. However, a third and relatively unexplored transport regime emerges when electron-electron interactions are sufficiently strong to induce a correlated and momentum-conserving charge flow similar to the Hagen-Poiseuille flow of a classical fluid. In the current work, we investigate the electronic signatures of such a viscous charge flow in high-mobility graphene FETs. In two complementary measurement schemes, we monitor differential resistance of graphene for different channel widths and for different effective electron temperatures. We observe a width dependence of channel conductivity and a minimum resistivity at elevated electron temperatures, indicative of the presence of charge hydrodynamics. By combining both approaches, the presence of viscous effects is verified in a temperature range starting from 178K and extending upto room temperature. Our experimental findings are supported by finite element calculations of the graphene channel. The presence of viscous effects at room temperature opens up avenues for functional hydrodynamic devices such as geometric rectifiers and charge amplifiers.