Ultrasensitive Calorimetric Measurements of the Electronic Heat Capacity of Graphene

Heat capacity is an invaluable quantity in condensed matter physics and yet has been completely inaccessible in two-dimensional (2D) van der Waals (vdW) materials, owing to their ultrafast thermal relaxation times and the lack of suitable nanoscale thermometers. Here, we demonstrate a novel thermal relaxation calorimetry scheme that allows the first measurements of the electronic heat capacity of graphene. It is enabled by combining a radio frequency Johnson noise thermometer, which can measure the electronic temperature with a sensitivity of ∼20 mK/Hz^1/2, and a photomixed optical heater that modulates T_e with a frequency of up to Ω = 0.2 THz. This allows record sensitive measurements of the electronic heat capacity C_e < 10 ^-19 J/K and the fastest measurement of electronic thermal relaxation time τ_e < 10 ^-12 s yet achieved by a calorimeter. These features advance heat capacity metrology into the realm of nanoscale and low-dimensional systems and provide an avenue for the investigation of their thermodynamic quantities.