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

Abstract

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.

Nonequilibrium Casimir–Polder Force between Nanoparticles and Graphene-Coated Silica Plate: Combined Effect of the Chemical Potential and Mass Gap

“…The analytic continuation of the polarization tensor to this region of the real frequency axis for a pristine and gapped graphene was performed in Refs. [67,70,71]. Here, we present the obtained results in a more convenient analytic form and generalize them for the case of gapped graphene with nonzero chemical potential.…”

“…This case is interesting from a theoretical point of view, but does not reflect realistic experimental situations. Next, the impact of the mass gap, which exists in real graphene sheets, on the nonequilibrium force was investigated [70]. Among other things, the mass gap necessary arises in graphene sheets deposited on some substrates.…”

“…An impact of the nonzero mass gap on the nonequilibrium Casimir-Polder interaction between nanoparticles and a freestanding in vacuum graphene sheet was investigated in Ref. [70] within the formalism of the polarization tensor. It was shown that, in this case, the nonequilibrium Casimir-Polder force remains attractive and it is possible to control its value by varying the mass-gap parameter.…”

“…It should be noted that computations of the nonequilibrium Casimir-Polder force acting on nanoparticles from real graphene sheets using the polarization tensor are rather cumbersome. They are connected with the calculation of the multiple integrals of rapidly varying functions and were realized on a supercomputer [70,71].…”

Nonequilibrium Casimir–Polder Interaction between Nanoparticles and Substrates Coated with Gapped Graphene

“…Taking into account that real graphene sheets are characterized by some energy gap, i.e., small but nonzero mass of quasiparticles [34], an impact of the energy gap on the nonequilibrium Casimir-Polder force between a nanoparticle and a freestanding gapped graphene sheet was investigated in [50]. It was shown that, by varying the energy gap, it is possible to control the force value.…”