Fast Energy Relaxation of Hot Carriers Near the Dirac Point of Graphene
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We investigate energy relaxation of hot Dirac fermions in monolayer and bilayer graphene devices. Conductance fluctuation thermometry is used to determine the effective carrier temperature at any current, and to compute the energy-loss rate and energy-relaxation time (τ e ). By determining the variation of τ e as a function of carrier density, we demonstrate a pronounced enhancement of energy relaxation (i.e. τ e → 0) as the Dirac point is approached from either the conduction or valence band. While this behavior is suggestive of recent theories for energy relaxation due to acoustic-phonon scattering, in both clean and disordered graphene, our observations imply a stronger density- ( n ) dependence (τ e ∝ n 4/3 ) than the n 1/2 1/2 variation predicted by these models. Similarly, while the temperature dependence of the energy-loss rate follows the T 3 variation predicted for super-collisions in disordered graphene, we demonstrate that the dependence of the relaxation time on temperature and density are not consistent with this mechanism. The temperature dependence of τ e is furthermore shown to follow a power-law decay of τ e α T -3/2in contrast to the T -1 variation reported previously for super-collisions. This variation is distinct, also, from the T -2 dependence predicted for direct acoustic-phonon scattering. We propose that the dramatic enhancement of the relaxation rate near the Dirac point may be consistent with ideas of charge puddling under disorder, suggesting that it becomes very difficult to excite carriers out of these localized regions. Our results therefore demonstrate how the peculiar properties of graphene extend also to the behavior of its non-equilibrium carriers.