Electronic Cooling in Graphene

Energy transfer to acoustic phonons is the dominant low-temperature cooling channel of electrons in a crystal. For cold neutral graphene we find that the weak cooling power of its acoustic modes relative to their heat capacity leads to a power-law decay of the electronic temperature when far from equilibrium. For heavily doped graphene a high electronic temperature is shown to initially decrease linearly with time at a rate proportional to $n^{3/2}$ with $n$ being the electronic density. The temperature at which cooling via optical phonon emission begins to dominate depends on graphene carrier density.

Figure 1

Equilibration of the electronic temperature. The evolution of the electronic temperature $T_e$ is plotted for electronic densities of (top to bottom) 0.02, 0.05, 0.1, 0.2, 0.3, and $0.4\times {10}^{12}{\mathrm{cm}}^{-2}$. The lattice temperature is 1 meV and the deformation potential is assumed to be 20 eV. The solid line corresponds to the equilibration of $T_e$ in a neutral system.

Figure 2

Equilibration of the chemical potential. As $T_e$ decreases (see Fig. 1), the chemical potential increases to preserve the electronic density.

Figure 3

The energy loss due to optical phonons divided by the energy loss do to acoustic phonons for neutral suspended graphene is plotted versus the electronic temperature for lattice temperatures of (bottom to top) 1, 10, 20, and 30 meV.

Figure 4

The analog of Fig. 3 for a doped system with $n={10}^{13}{\mathrm{cm}}^{-2}$.