Measurement 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 a lack of calorimeters capable of operating at nanoscale. Here, we develop a proof-of-concept electronic calorimeter with record sensitivity (< 10^-20 J/K) by combining a ~20 mK/Hz^1/2–sensitive Johnson-noise thermometer with a novel optical heater operating in the low terahertz frequency domain. It measures thermal conductance G_th of nanoscale cooling pathways and temperature relaxation time τ of the system in a niche range of 0.5 picosecond to 1 nanosecond, accessing orders of magnitude faster relaxation than previous state-of-the-art calorimeters, and thereby determines the heat capacity C = τG_th. We demonstrate the first ever measurement of electronic specific heat of graphene, and verify its ultra-low magnitude and proportionality to carrier density and temperature down to 15 K with a record resolution of 36 k_B/μm². This calorimetry technique can be implemented on other 2D vdW materials and devices based thereof, unlocking a new and powerful approach to their research.