We present a theoretical description of energy transfer processes between two noncontact quasi-two-dimensional crystals separated by distance $a$, oscillating with frequency ${\omega }_0$ and amplitude ${\rho }_0$, and compare it with the case of two quasi-two-dimensional crystals in uniform parallel motion. We apply the theory to calculate van der Waals energy and dissipated energy in two oscillating slabs where each slab consists of a graphene monolayer deposited on ${\mathrm{SiO}}_2$ substrate. The graphene dielectric response is determined from first principles, and ${\mathrm{SiO}}_2$ surface response is described using empirical local dielectric function. We studied the modification of vdW attraction as a function of the driving frequency and graphene doping. We propose the idea of controlling the binding energy between two slabs by tuning the graphene dopings $E_{Fi}$ and driving frequency ${\omega }_0$. We found simple ${\rho }_0^2$ dependence of vdW and dissipated energy. As the Dirac plasmons of frequency ${\omega }_p$ are the dominant channels through which the energy between slabs can be transferred, the dissipated power in equally doped $E_{F1}=E_{F2}\ne 0$ graphenes shows strong ${\omega }_0=2{\omega }_p$ peak. This peak is substantially reduced when graphenes are deposited on the ${\mathrm{SiO}}_2$ substrate. If only one graphene is pristine ($E_{Fi}=0$) the $2{\omega }_p$ peak disappears. For larger separations $a$ the phononic losses also become important and the doping causes shifts, appearance, and disappearance of many peaks originating from resonant coupling between hybridized electronic/phononic excitations in graphene/substrate slabs.

• Received 7 March 2018
• Revised 7 August 2018

DOI:https://doi.org/10.1103/PhysRevB.98.125405