Ultra-sensitive thermal measurements of graphene: pathway to single microwave photon detector

As a result of the linear energy spectrum and low dimensionality, electrons in graphene have astoundingly small thermal conductance and heat capacitance. By developing a large bandwidth, high sensitivity Johnson noise measurement technique at microwave frequency, we can measure the temperature of graphene electrons down to a precision of 0.1 mK within 1 second. This enables us to study the thermal properties of this wonder material: for instance, we have measured the energy transfer from electrons to phonons at 1 pW/K $\mu$m$^2$ level and a record-low heat capacity, only about 100 kB/$\mu$m$^2$, at low temperature. We have applied these exotic thermal quantities to make a graphene bolometer and mixer. Our measurement data agree well with the theory that the proposed graphene caloriometer should have single photon sensitivity from IR down to microwave regime at ultra-low temperature.