Hydrodynamics and Viscous Flow in Graphene Measured with Johnson Noise Thermometry

Abstract

In this dissertation, we investigate thermal transport phenomena in 2-dimensional monolayer and bilayer graphene, both of which are candidates for strongly interacting, correlated electronic systems. The interactions between electrons in solid-state materials give rise to novel states of matter, leading to new theoretical developments and device applications. Measurement of thermal transport in such systems can reveal exotic physics in these new states that may be elusive to electrical transport, such as charge-neutral transport modes or collective behavior. One particular emergent phenomenon that has recently attracted significant attention is the viscous hydrodynamic transport regime, where particles’ behavior is best collectively described as a viscous fluid rather than as individual particles. The recent discovery of this regime in graphene has driven new devices and insights about other materials as well.

Accordingly, several strongly-interacting electronic systems in addition to graphene have recently been both predicted and shown experimentally to exhibit a ratio of thermal conductivity to electrical conductivity that deviates from the near-universal Wiedemann-Franz law. Monolayer and bilayer graphene both present a strong opportunity for using thermal transport to study the interplay of quantum criticality and hydrodynamics due to a combination of intrinsic material properties and recent advances in low-disorder sample preparation. However, despite previous experimental work, the Lorenz ratio suppression in doped graphene remains largely experimentally unstudied, and the viscous analogue of Joule heating remains entirely unexplored, limiting the real-life applications of electron hydrodynamics in devices.

To perform the thermal transport measurements, we have developed a Johnson noise thermometry measurement technique applicable to mesoscopic devices with variable source impedance with high bandwidth for fast data acquisition. We thoroughly discuss the details of the technique, including differential noise measurements, two-stage impedance matching, cryogenic circuitry components, calibration, and measurement. Most importantly, we have discovered and studied several parasitic effects in the noise measurement technique that could significantly reduce the measurement accuracy, and we discuss our novel methods to quantify and mitigate them. As a demonstration, we measure thermal conductivity on a bilayer graphene sample spanning the metallic and semiconducting regimes over a wide resistance range.

We use our advanced Johnson noise techniques to study hydrodynamics in monolayer and bilayer graphene, both at charge neutrality and in the doped regime, by searching for breakdowns of the Wiedemann-Franz law. We find that while both systems show some evidence of Lorenz ratio enhancement at charge neutrality and suppression at small doping, the evidence varies significantly from device to device due to the prevailing contact resistance, ballistic transport, and phonon-cooling, requiring careful consideration for quantitative analysis. We provide a systematic diagnosis and potential remedies for these technical challenges.

To explore viscous hydrodynamics further from a novel perspective, we use a combination of electrical and noise-based thermal magneto-transport measurements in the Corbino geometry to study viscosity directly. We find a new experimental signature of viscous heating leading to magnetically-induced redistribution of temperature, an effect that is coincident in temperature and density with the aforementioned Lorenz ratio suppression. These two effects thus provide robust qualitative signatures of hydrodynamics, despite arising from two distinct aspects of this regime: microscopic momentum conservation due to electron-electron scattering, and geometry-dependent viscous dissipation. Our results mark the first observation of viscous electronic heating in an electron fluid, which may influence the design of hydrodynamic devices and offers a new methodology to identify hydrodynamic states in other systems.