Electronic Thermal Conductance of Graphene via Electrical Noise

Abstract

This dissertation presents the methods and experimental results of studies on electronic thermal transport in mesoscopic conductors by means of radio frequency Johnson noise thermometry. In particular, we present the application of these methods to study the electronic thermal conductivity of monolayer graphene over a wide range of temperatures, charge densities, and magnetic fields. A comprehensive theory of thermal noise in conductors is formulated in a language convenient for high frequency measurements of mesoscopic samples. Auto- and cross-correlated Johnson noise thermometry is demonstrated over the temperature range of 3 − 300 K and in magnetic fields up to 13 T , achieving a sensitivity of 5.5 mK (110 ppm) in 1 s of integration time. Techniques for overcoming the challenges of measuring devices with resistances that dynamically vary over multiple orders of magnitude are presented. Impedance matching circuits, capable of withstanding the harsh measurement environments of condensed matter experiments while remaining stable across the extreme changes in temperature and magnetic field, are described. A systematic and robust calibration procedure for converting noise power to electronic temperature is outlined which allows for the inevitable drift of device resistance that often plagues mesoscopic experiments. With the ability to measure electronic temperature, the thermal conductance between the electronic system and a thermal bath can be measured. We quantitatively discuss the various cooling mechanisms of the quasi-relativistic electrons in graphene and how they combine to create a complicated thermal network. Moreover, we present experimental techniques to disentangle these mechanisms allowing the study of each cooling path way independently. Using these methods, the electron-phonon coupling of clean graphene is quantitatively compared to theoretical estimates and found to be an order of magnitude larger than that predicted for graphene intrinsic acoustic-phonons and the disorder-assisted supercollision mechanism. We find that at low temperature and high carrier density, the thermal conductivity of diffusive monolayer graphene closely obeys the Wiedemann-Franz law. Near the charge neutrality point, we present evidence that the electronic system in monolayer graphene forms an electron-hole plasma with collective behavior described by hydrodynamics. This charge-neutral plasma of quasi-relativistic fermions, known as a Dirac fluid, exhibits a substantial enhancement of the thermal conductivity, due to decoupling of charge and heat currents. We report an order of magnitude increase in the thermal conductivity and the breakdown of the Wiedemann -Franz law in the thermally populated charge-neutral plasma in graphene. A novel hydrodynamic framework in the presence of charge disorder — in the form of a spatially varying chemical potential — is presented and compared quantitatively to our experimental results. Lastly, measurements for the low temperature thermal conduction of graphene under a magnetic field are presented. We report data spanning from zero field, through the quantum oscillation regime, and into the quantum Hall regime.