How many-body effects modify the van der Waals interaction between graphene sheets

Undoped graphene (Gr) sheets at low temperatures are known, via Random Phase Approximation (RPA) calculations, to exhibit unusual van der Waals (vdW) forces. Here we show that graphene is the first known system where effects beyond the RPA make qualitative changes to the vdW force. For large separations, $D \gtrsim 10$nm where only the $\pi_z$ vdW forces remain, we find the Gr-Gr vdW interaction is substantially reduced from the RPA prediction. Its $D$ dependence is very sensitive to the form of the long-wavelength many-body enhancement of the velocity of the massless Dirac fermions, and may provide independent confirmation of the latter via direct force measurements.