Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation

Lifshitz-type formulas for graphene and single-wall carbon nanotubes: van der Waals and Casimir interations

Lifshitz-type formulas are obtained for the van der Waals and Casimir interaction between graphene and a material plate, graphene and an atom or a molecule, and between a single-wall carbon nanotube and a plate. The reflection properties of electromagnetic oscillations on graphene are governed by the specific boundary conditions imposed on the infinitely thin positively charged plasma sheet, carrying a continuous fluid with some mass and charge density. The obtained formulas are applied to graphene interacting with Au and Si plates, to hydrogen atoms and molecules interacting with graphene, an…

The Casimir-Polder interaction of an atom and real graphene sheet: Verification of the Nernst heat theorem

We find the low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with real graphene sheet possessing nonzero energy gap and chemical potential. Employing the formalism of the polarization tensor, it is shown that the Casimir-Polder entropy goes to zero by the power law with vanishing temperature, i.e., the Nernst heat theorem is satisfied. This result is discussed in connection with the problems connected with account of free charge carriers in the Lifshitz theory.

Casimir Force between Atomically Thin Gold Films

We have used density functional theory to calculate the anisotropic dielectric functions for ultrathin gold sheets (composed of 1, 3, 6, and 15 atomic layers). Such films are important components in nano-electromechanical systems. When using correct dielectric functions rather than bulk gold dielectric functions we predict an enhanced attractive Casimir-Lifshitz force (at most around 20%) between two atomically thin gold sheets. For thicker sheets the dielectric properties and the corresponding Casimir forces approach those of gold half-spaces. The magnitude of the corrections that we predict …

Nernst heat theorem for the thermal Casimir interaction between two graphene sheets

We find analytic asymptotic expressions at low temperature for the Casimir free energy, entropy and pressure of two parallel graphene sheets in the framework of the Lifshitz theory. The reflection coefficients of electromagnetic waves on graphene are described on the basis of first principles of quantum electrodynamics at nonzero temperature using the polarization tensor in (2+1)-dimensional space-time. The leading contributions to the Casimir entropy and to the thermal corrections to the Casimir energy and pressure are given by the thermal correction to the polarization tensor at nonzero Mats…

悬浮石墨烯上的强排斥性Lifshitz-van der Waals力

Strong Repulsive Lifshitz-van der Waals Forces on Suspended Graphene

本文通过原子力显微镜直接测量了悬浮石墨烯表面由量子涨落与二维单层原子厚度及双折射耦合产生的强排斥性Lifshitz-vdW力，在8.8 nm间距处达1.4 kN/m²，揭示悬浮二维材料具有本征排斥表面和显著降低的润湿性。

Origin of large thermal effect in the Casimir interaction between two graphene sheets

Using the recently derived representation for the polarization tensor in (2+1)-dimensional space-time allowing an analytic continuation to the entire plane of complex frequencies, we obtain simple analytic expressions for the reflection coefficients of graphene at nonzero Matsubara frequencies. In the framework of the Lifshitz theory, these coefficients are shown to lead to nearly exact results for the Casimir free energy and pressure between two graphene sheets. The constituent parts of large thermal effect, arising in the Casimir interaction at short separations due to an explicit parametric…

Coulomb scattering in the Born approximation and the use of generalized functions

We discuss three ways of obtaining the Born approximations for Coulomb scattering: The standard way, making use of a convergence factor ("screening"), Oppenheimer's way using cylindrical (instead of spherical) coordinates, and finally Landau and Lifshitz' way. The last one although it does require some background from the theory of generalized functions is nevertheless a very instructive and important technique deserving more exposure to physicists.

具有能隙和掺杂的石墨烯对原子或纳米粒子的Casimir-Polder力：大间距下的渐近行为

Casimir-Polder Force on Atoms or Nanoparticles from the Gapped and Doped Graphene: Asymptotic Behavior at Large Separations

本文在Lifshitz理论框架下研究具有能隙和化学势的石墨烯对原子或纳米粒子的Casimir-Polder力，推导了大间距下零频项的解析渐近表达式，并揭示了石墨烯经典极限与零频项大间距极限之间的差异及其对能隙和化学势的依赖关系。

质量隙对纳米粒子与石墨烯在非热平衡下色散相互作用的影响

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

本文基于推广的Lifshitz理论和Dirac模型，研究了带隙石墨烯与纳米粒子在非热平衡条件下的色散力，发现质量隙使非平衡力保持吸引特性，为微纳器件设计提供理论依据。

Casimir pressure in peptide films on metallic substrates: Change of sign via graphene coating

We find that the Casimir pressure in peptide films deposited on metallic substrates is always repulsive which makes these films less stable. It is shown that by adding a graphene sheet on top of peptide film one can change the sign of the Casimir pressure by making it attractive. For this purpose, the formalism of the Lifshitz theory is extended to the case when the film and substrate materials are described by the frequency-dependent dielectric permittivities, whereas the response of graphene to the electromagnetic field is governed by the polarization tensor in (2+1)-dimensional space-time f…

Strong thermal and electrostatic manipulation of the Casimir force in graphene multilayers

We show that graphene-dielectric multilayers give rise to an unusual tunability of the Casimir-Lifshitz forces, and allow to easily realize completely different regimes within the same structure. Concerning thermal effects, graphene-dielectric multilayers take advantage from the anomalous features predicted for isolated suspended graphene sheets, even though they are considerably affected by the presence of the dielectric substrate. They can also archive the anomalous non-monotonic thermal metallic behavior by increasing the graphene sheets density and their Fermi energy. In addition to a stro…

Dispersion Interaction of Atoms with Single-Walled Carbon Nanotubes described by the Dirac Model

We calculate the interaction energy and force between atoms and molecules and single-walled carbon nanotubes described by the Dirac model of graphene. For this purpose the Lifshitz-type formulas adapted for the case of cylindrical geometry with the help of the proximity force approximation are used. The results obtained are compared with those derived from the hydrodymanic model of graphene. Numerical computations are performed for hydrogen atoms and molecules. It is shown that the Dirac model leads to larger values of the van der Waals force than the hydrodynamic model. For a hydrogen molecul…

The Casimir effect in graphene systems: Experiment and theory

The Casimir effect in graphene systems is reviewed with emphasis made on the large thermal correction to the Casimir force predicted at short separations between the test bodies. The computational results for the Casimir pressure and for the thermal correction are presented for both pristine graphene and real graphene sheets, which possess nonzero energy gap and chemical potential, obtained by means of exact polarization tensor. Two experiments on measuring the gradient of the Casimir force between an Au-coated sphere and graphene- coated substrates performed by using a modified atomic force m…