Electron heating and mechanical properties of graphene

The heating of electrons in graphene by laser irradiation, and its effects on the lattice structure, are studied. Values for the temperature of the electron system in realistic situations are obtained. For sufficiently high electron temperatures, the occupancy of the states in the $\sigma$ band of graphene is modified. The strength of the carbon-carbon bonds changes, leading to the emergence of strains, and to buckling in suspended samples. While most applications of “strain engineering” in two-dimensional materials focus on the effects of strains on electronic properties, the effect studied here leads to alterations of the structure induced by light. This optomechanical coupling can induce deflections in the order of $\sim 50$ nm in micron-sized samples.

Figure 1

Schematic drawing of the device used to heat up electrons in a graphene lattice. The substrate is depicted in gray and has a hole. A region of suspended graphene is illuminated by a laser beam (depicted in green) of radius $R$.

Figure 2

Power dissipated by optical phonons over an area $A=1\mu {\mathrm{m}}^2$ as a function of electron temperature.

Figure 3

Temperature of the electron-hole plasma vs laser power for a laser spot of radius $R=1\mu \mathrm{m}$. Red: Dissipation by electronic heat diffusion. Blue: Dissipation by optical phonon absorption. Black: Total dissipation. For a laser power of $W=5$ mW, the calculated temperature is $T=2250$ K.

Figure 4

Equilibrium lattice constant (blue) and gap between the $\sigma$ bands (red) vs electronic temperature.

Figure 5

Profile of a disk-shaped suspended graphene flake with clamped edges of radius $R=5000$ nm with a thermally generated stress of $\epsilon =0.01\%$.

Figure 6

As in Fig. 3 for a graphene bilayer. The calculated temperature is $T\approx 4570$ K.