  Hot electron effects in graphene are significant because of graphene's small
electronic heat capacity and weak electron-phonon coupling, yet the dynamics
and cooling mechanisms of hot electrons in graphene are not completely
understood. We describe a novel photocurrent spectroscopy method that uses the
mixing of continuous-wave lasers in a graphene photothermal detector to measure
the frequency dependence and nonlinearity of hot-electron cooling in graphene
as a function of the carrier concentration and temperature. The method offers
unparalleled sensitivity to the nonlinearity, and probes the ultrafast cooling
of hot carriers with an optical fluence that is orders of magnitude smaller
than in conventional time-domain methods, allowing for accurate
characterization of electron-phonon cooling near charge neutrality. Our
measurements reveal that near the charge neutral-point the nonlinear power
dependence of the electron cooling is dominated by disorder-assisted
collisions, while at higher carrier concentrations conventional
momentum-conserving cooling prevails in the nonlinear dependence. The relative
contribution of these competing mechanisms can be electrostatically tuned
through the application of a gate voltage -- an effect that is unique to
graphene.
