Impact of Mass-Gap on the Dispersion Interaction of Nanoparticles with Graphene out of Thermal Equilibrium

We consider the nonequilibrium dispersion force acting on nanoparticles on the source side of a gapped graphene sheet. Nanoparticles are kept at the environmental temperature, whereas the graphene sheet may be either cooler or hotter than the environment. Calculation of the dispersion force as a function of separation at different values of the mass-gap parameter is performed using the generalization of the fundamental Lifshitz theory to out-of-thermal-equilibrium conditions. The response of the gapped graphene to quantum and thermal fluctuations in the electromagnetic field is described by the polarization tensor in (2+1)-dimensional space-time in the framework of the Dirac model. The explicit expressions for the components of this tensor in the area of evanescent waves are presented. The nontrivial impact of the mass-gap parameter of graphene on the nonequilibrium dispersion force, as compared to the equilibrium one, is determined. It is shown that, unlike the case of pristine graphene, the nonequilibrium force preserves an attractive character. The possibilities of using the obtained results in the design of micro- and nanodevices, incorporating nanoparticles and graphene sheets for their functionality, is discussed.

Automated summary

The nonequilibrium dispersion force acting on nanoparticles on the source side of a gapped graphene sheet is investigated in this study. The dispersion force is calculated as a function of separation at different mass-gap parameters using the generalization of the Lifshitz theory. The response of the graphene sheet to quantum and thermal fluctuations is described using the polarization tensor in (2+1)-dimensional space-time based on the Dirac model. The nontrivial impact of the mass-gap parameter on the nonequilibrium dispersion force, as well as its potential applications in micro- and nanodevice design, are discussed.