Ultra-fast calorimetric measurements of the electronic heat capacity of graphene

Heat capacity is an invaluable quantity in condensed matter physics, yet it has been so far experimentally inaccessible in two-dimensional (2D) van der Waals (vdW) materials, owing to their ultra-fast thermal relaxation times and the lack of suitable nano-scale thermometers. Here, we demonstrate a novel thermal relaxation calorimetry scheme that allows the first measurements of the electronic heat capacity of graphene Ce. It is enabled by the grouping of a radio-frequency Johnson noise thermometer, which can measure the electronic temperature Te with a measurement sensitivity of {\delta}Te ~ 20 mK, and an ultra-fast photo-mixed optical heater, which can simultaneously modulate Te with a frequency of up to {\Omega}=0.2 THz. This combination allows record sensitive and record fast measurements of the electronic heat capacity Ce < 10^(-19) J/K, with an electronic thermal relaxation time {\tau}e < 10^(-13), representing orders of magnitude improvements as compared to previous state-of-the-art calorimeters. These features embody a breakthrough in heat capacity metrology of nano-scale and low-dimensional systems, and provide a new avenue for the investigation of their thermodynamic quantities.