Electron viscosity and device-dependent variability in four-probe electrical transport in ultra-clean graphene field-effect transistors

Abstract

Hydrodynamic electrons in high-mobility graphene devices have demonstrated great potential in establishing an electronic analogue of relativistic quantum fluid in solid-state systems. One of the key requirements for observing viscous electron flow in an electronic channel is a large momentum-relaxation path, a process primarily limited by electron-impurity/phonon scattering in graphene. Over the past decade, multiple complex device geometries have been successfully employed to suppress momentum-relaxing scattering mechanisms; however, experimental observations have been found to be sensitive to the device fabrication process and architecture, raising questions about the signature of electron hydrodynamics itself. Here, we present a study on multiple ultra-clean graphene field-effect transistors (FETs) in a simple, rectangular four-terminal device architecture. Using electrical transport measurements, we have characterised the pristine quality of the graphene FETs and examined the variation of electrical resistance in the doped regime as a function of carrier density and temperature. Our results reveal strong device-dependent variability even in the most simple architecture that we attribute to competing momentum-conserving and momentum-relaxing scattering mechanisms, as well as coupling to contacts. Further, we have proposed a phenomenological method for analysing the results, which yields transport parameters in accordance with recent experiments. This simple experimental strategy and analysis can serve as an efficient tool for extracting the viscous electronic contribution in state-of-the-art high-mobility graphene FETs.