Quantum friction between graphene sheets

We study the Casimir friction phenomenon in a system consisting of two flat, infinite, and parallel graphene sheets, which are coupled to the vacuum electromagnetic (EM) field. Those couplings are implemented, in the description we use, by means of specific terms in the effective action for the EM field. They incorporate the distinctive properties of graphene, as well as the relative sliding motion of the sheets. Based on this description, we evaluate two observables due to the same physical effect: the probability of vacuum decay and the frictional force. The system exhibits a threshold for frictional effects; namely, they only exist if the speed of the sliding motion is larger than the Fermi velocity of the charge carriers in graphene.

Figure 1

Imaginary part of the effective action per unit of time and area, as a function of the relative velocity of the plate, for a typical graphene Fermi velocity $v_F=0.003$, in units of $A=\frac{{\alpha }_N^2}{32{\pi }^2}\frac{1}{a^3}$.

Figure 2

Modulus of the transversal and longitudinal contributions to the force per unit of area $F_{\mathrm{fr}}$ acting on the plate as a function of its relative velocity, for a typical graphene Fermi velocity $v_F=0.003$. The force is normalized by the static Casimir force between the plates.

Figure 3

Modulus of the force per unit of area acting on the plate as a function of its relative velocity, for velocities close to the Fermi velocity of graphene, $v_F=0.003$. The force is normalized by the static Casimir force between the plates.