Graphene is a material with remarkable electronic properties[1] and exceptional thermal transport
properties near room temperature, which have been well examined and understood[2, 3].
However at very low temperatures the thermodynamic and thermal transport properties are much
less well explored[4, 5] and somewhat surprisingly, is expected to exhibit extreme thermal isolation.
Here we demonstrate an ultra-sensitive, wide-bandwidth measurement scheme to probe the
thermal transport and thermodynamic properties of the electron gas of graphene. We employ
Johnson noise thermometry at microwave frequency to sensitively measure the temperature of the
electron gas with resolution of 4mK/√Hz and a bandwidth of 80 MHz. We have measured the
electron-phonon coupling from 2-30 K at a charge density of 2 •10^(11)cm^(-2). Utilizing bolometric
mixing, we have sensed temperature oscillations with period of 430 ps and have determined the
heat capacity of the electron gas to be 2 • 10^(-21)J/(K •µm^2) at 5 K which is consistent with that
of a two dimensional, Dirac electron gas. These measurements suggest that graphene-based devices
together with wide bandwidth noise thermometry can generate substantial advances in the
areas of ultra-sensitive bolometry[6], calorimetry[7], microwave and terahertz photo-detection[8],
and bolometric mixing for applications in areas such as observational astronomy[9] and quantum
information and measurement[10]
