Abstract
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.
Highlights
For large separations D ≳ 10 nm, where only the πz van der Waals (vdW) forces remain, we find that 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, in-plane many-body enhancement of the velocity of the massless Dirac fermions and may provide independent confirmation of the latter via direct force measurements
It is well known that a zero-gap conical πz electronic Bloch band structure of undoped graphene, supporting massless Dirac fermions propagating with speed v, should give this system a number of unusual properties [1]
Summary
It is well known that a zero-gap conical πz electronic Bloch band structure of undoped graphene, supporting massless Dirac fermions propagating with speed v, should give this system a number of unusual properties [1] One such property relates to the low-temperature dispersion [van der Waals (vdW)] interaction energy per unit area. Plot of the function F that controls, via Eq (3), the value of the constant C3 for the RPA van der Waals interaction between graphene sheets In this context, it is important to note that for real graphene, Eq (2) is valid only at large separations: At shorter distances, gapped transitions other than the πz → πÃz contribute a vdW energy of the conventional form [Eq (1)]. At these separations, all electrostatic and metallic overlap forces have long vanished
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