Electron Viscosity and Device-Dependent Variability in Four-Probe Electrical Transport in Ultraclean Graphene Field-Effect Transistors

Electrons in high-mobility graphene devices have demonstrated great potential in establishing an electronic analogue of relativistic quantum fluid in solid-state systems. Over the past decade, complex device geometries have been employed to enable experimental detection of viscous electronic flow; however, the observations have been found to be sensitive to the device architecture and fabrication process, raising questions about the signature of electron hydrodynamics itself. Here, we present a study on multiple ultraclean graphene field-effect transistors (FETs) in a rectangular four-terminal device architecture. Using electrical transport measurements, we have examined variation of the electrical resistance of FETs in the doped regime as a function of the carrier density and temperature. Our results reveal strong device-dependent variability, attributed to competing momentum-conserving and momentum-relaxing scattering mechanisms. Further, we have proposed a phenomenological method for analyzing the results, yielding transport parameters consistent with recent theory and experiments.