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We evaluate the van der Waals (vdW) interaction energy at zero temperaturebetween two undoped strained graphene layers separated by a finite distance. Weconsider the following three models for the anisotropic case: (a) where one ofthe two layers is uniaxially strained, (b) the two layers are strained in thesame direction, and (c) one of the layers is strained in the perpendiculardirection with respect to the other. We find that for all three models andgiven value of the electron-electron interaction coupling, the vdW interactionenergy increases with increasing anisotropy. The effect is most striking forthe case when both layers are strained in the same direction where we observeup to an order of magnitude increase in the strained relative to the unstrainedcase. We also investigate the effect of electron electron interactionrenormalization in the region of large separation between the strained graphenelayers. We find that the many-body renormalization contributions to thecorrelation energy are non negligible and the vdW interaction energy decreasesas a function of increasing distance between the layers due to renormalizationof the Fermi velocity, the anisotropy, and the effective interaction. Ouranalysis can be useful in designing novel graphene-based vdW heterostructureswhich, in recent times, has seen an upsurge in research activity.

Van der Waals forces and electron-electron interactions in two strained graphene layers