Electronic Thermal Conductance Measurement of Ultraclean Bilayer Graphene using Johnson Noise Thermometry*

Strongly interacting electron systems can exhibit exotic new physics, such as the hydrodynamic regime, where particles' behavior is best described as a viscous fluid rather than as individual particles. Several such hydrodynamic systems have recently been both predicted and shown experimentally to violate the Wiedemann Franz (WF) law, and the link between hydrodynamic transport and the violation of WF has been explored. In this study, we investigate thermal conductance in ultraclean bilayer graphene samples as a function of temperature, carrier density, and displacement field. We measure thermal conductance by Joule-heating the graphene and measuring its resulting thermal response via Johnson noise thermometry. We collect Johnson noise over a several hundred MHz bandwidth, improving upon our previously-developed noise measurement technique with cryogenic low-noise amplifiers and symmetric LC matching circuits. Measuring the zero-bias Johnson noise of the device at several bath temperatures allows us to calibrate the effective gain and system noise for several orders of magnitude of device resistance. Our data shows an enhancement of the thermal conductance above the value predicted by the WF law near the charge neutrality point.