he Casimir force is calculated between plates with thin metallic coating. Thin films are described with spatially dispersive (nonlocal) dielectric functions. For thin films the nonlocal effects are more relevant than for half-spaces. However, it is shown that even for film thickness smaller than the mean free path for electrons, the difference between local and nonlocal calculations of the Casimir force is of the order of a few tenths of a percent. Thus the local description of thin metallic films is adequate within the current experimental precision and range of separations.
We present theoretical calculations of the Casimir force for Au thin films near the insulator-conductor transition that has been observed experimentally. The dielectric function of the Au thin films is described by the Drude-Smith model. The parameters needed to model the dielectric function such as the relaxation time, plasma frequency and the backscattering constant depend on the thickness of the film. The Casimir force decreases as the film thickness decreases until it reaches a minimum after which the force increases again. The minimum of the force coincides with the critical film thicknes…
We derive an analytic behavior of the Casimir free energy, entropy and pressure of metallic films in vacuum at low temperature. It is shown that this behavior differs significantly depending on whether the plasma or the Drude model is used to describe the dielectric properties of film metal. For metallic films described by the lossless plasma model the thermal corrections to the Casimir energy and pressure drop to zero exponentially fast with increasing film thickness. There is no classical limit in this case. The Casimir entropy satisfies the Nernst heat theorem. For metallic films with perfe…
The Casimir force is calculated between Au thin films that are described by a Drude model with a frequency dependent damping function. The model parameters are obtained from available experimental data for Au thin films. Two cases are considered; annealed and nonannealed films that have a different damping function. Compared with the calculations using a Drude model with a constant damping parameter, we observe changes in the Casimir force of a few percent. This behavior is only observed in films of no more than 300 $Å$ thick.
We present results of first principle calculations of the Casimir force between Si films of nanometric size, which show that it depends significantly upon the configuration of the surface atoms, and give evidence of the importance of surface states.
The frequency spectrum of the finite temperature correction to the Casimir force can be determined by the use of the Lifshitz formalism for metallic plates of finite conductivity. We show that the correction for the TE electromagnetic modes is dominated by frequencies so low that the plates cannot be modelled as ideal dielectrics. We also address the issues relating to the behavior of electromagnetic fields at the surfaces an within metallic conductors, and claculate the surface modes using appropriate low-frequency metallic boundary conditions. Our result brings the tehrmal correction into ag…
The frequency spectrum of the finite temperature correction to the Casimir force can be determined by use of the Lifshitz formalism for metallic plates of finite conductivity. We show that the correction for the $TE$ electromagnetic modes is dominated by frequencies so low that the plates cannot be modelled as ideal dielectrics. We also address issues relating to the behavior of electromagnetic fields at the surfaces and within metallic conductors, and calculate the surface modes using appropriate low-frequency metallic boundary conditions. Our result brings the thermal correction into agreeme…
We investigate the role of size quantization in the vacuum force between metallic films of nanometric thickness. The force is calculated by the Lifshitz formula with the film dielectric tensor derived from the one-electron energies and wavefunctions under the assumption of a constant potential inside the film and a uniform distribution of the positive ion charge. The results show that quantization effects tend to reduce the force with respect to the continuum plasma model. The reduction is more significant at low electron densities and for film size of the order of few nanometers and persists …
Optical properties of the deposited gold films are discussed in connection with the Casimir force prediction. Voids in the films and electron scattering on the grain boundaries reduce the force at small separations on the 2% level in comparison with the bulk material prediction. The contribution of the patch potential due to polycrystalline structure of the films is shown to be small for the existing Casimir force experiments.
The Casimir free energy and pressure of thin metal films deposited on metallic plates are considered using the Lifshitz theory and the Drude and plasma model approaches to the role of conduction electrons. The bound electrons are taken into account by using the complete optical data of film and plate metals. It is shown that for films of several tens of nanometers thickness the Casimir free energy and pressure calculated using these approaches differ by hundreds and thousands percent and can be easily discriminated experimentally. According to our results, the free energy of a metal film does …
We examine the Casimir free energy and pressure of magnetic metal films, which are free-standing in vacuum, sandwiched between two dielectric plates, and deposited on either nonmagnetic or magnetic metallic plates. All calculations are performed using both the Drude and plasma model approaches to the Lifshitz theory. According to our results, the Casimir free energies and pressures calculated using both theoretical approaches are significantly different in the magnitude and sign even for thin films of several tens of nanometers thickness. Thus, for the Ni film of 47\,nm thickness deposited on …
We investigate the thermal Casimir force between two parallel plates made of different isotropic materials which are separated by a uniaxial anisotropic film. Numerical computations of the Casimir pressure at T=300K are performed using the complete Lifshitz formula adapted for an anisotropic intervening layer and in the nonrelativistic limit. It is shown that the standard (nonrelativistic) theory of the van der Waals force is not applicable in this case, because the effects of retardation contribute significantly even for film thicknesses of a few nanometers. We have also obtained simple analy…
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 …
The Casimir free energy of dielectric films, both free-standing in vacuum and deposited on metallic or dielectric plates, is investigated. It is shown that the values of the free energy depend considerably on whether the calculation approach used neglects or takes into account the dc conductivity of film material. We demonstrate that there are the material-dependent and universal classical limits in the former and latter cases, respectively. The analytic behavior of the Casimir free energy and entropy for a free-standing dielectric film at low temperature in found. According to our results, th…
We investigate the Casimir free energy of a metallic film either sandwiched between two dielectric plates or in vacuum. It is shown that even for a thin film of several tens of nanometer thickness the Casimir free energy and pressure calculated with the Lifshitz theory using the Drude model and the plasma model approaches take significantly different values and can be easily discriminated. According to our results, the classical limit is already achieved for films of about 100\,nm thickness if the Drude model approach is used in calculations. In this case the classical expressions for the Casi…
We have performed comparative measurements of the Casimir force between a metallic plate and a transparent sphere coated with metallic films of different thicknesses. We have observed that, if the thickness of the coating is less than the skin-depth of the electromagnetic modes that mostly contribute to the interaction, the force is significantly smaller than that measured with a thick bulk-like film. Our results provide the first direct evidence of the skin-depth effect on the Casimir force between metallic surfaces.
The Casimir free energy of peptide films on a silicon substrate: Impact of dielectric-to-metal transition in silicon and nanoparticles in peptide
Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences（俄罗斯科学院普尔科沃中央天文台）；Peter the Great Saint Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
We present complete results of the experiment on measuring the Casimir force between an Au-coated sphere and an untreated or, alternatively, UV-treated indium tin oxide film deposited on a quartz substrate. Measurements were performed using an atomic force microscope in a high vacuum chamber. The measurement system was calibrated electrostatically. Special analysis of the systematic deviations is performed, and respective corrections in the calibration parameters are introduced. The corrected parameters are free from anomalies discussed in the literature. The experimental data for the Casimir …
The Casimir interaction between two thin material films, between a film and a thick plate and between two films deposited on substrates is considered at large separations (high temperatures) which correspond to the classical limit. It is shown that the free energy of the classical Casimir interaction between two insulating films with no free charge carriers and between an insulating film and a material plate depends on film thicknesses and decreases with separation more rapidly than the classical limit for two thick plates. The free energy of thin films characterized by the metallic-type diele…
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…
Recently V. A. Yampol'skii, S. Savel'ev, Z. A. Mayselis, S. S. Apostolov, and F. Nori [Phys. Rev. Lett., v.101, 096803 (2008),arXiv:0712.1395] claimed that the Casimir force between a thin metal film described by the Drude model and an ideal metal semispace can decrease with temperature whereas for bulk samples the Casimir force increases with temperature. On this basis the experimental observation of the decreasing temperature dependence of the Casimir force magnitude between a film and a bulk ideal metal was proposed. We demonstrate that, contrary to what is claimed by the authors, the magni…
We propose an approach for investigation of interaction of thin material films with quantum electrodynamic fields. Using main principles of quantum electrodynamics (locality, gauge invariance, renormalizability) we construct a single model for Casimir-like phenomena arising near the film boundary on distances much larger then Compton wavelength of the electron where fluctuations of Dirac fields are not essential. In this model the thin film is presented by a singular background field concentrated on a 2-dimensional surface. All properties of the film material are described by one dimensionless…
A significant decrease in the magnitude of the Casimir force (from 21% to 35%) was observed after an indium tin oxide (ITO) sample interacting with an Au sphere was subjected to the UV treatment. Measurements were performed by using an atomic force microscope (AFM) in high vacuum. The experimental results are compared with theory, and a hypothetical explanation for the observed phenomenon is proposed.
We derive analytic expressions for the classical Casimir-Polder free energy and force for a polarizable (magnetizable) atom (microparticle) interacting with thin films, made of different materials, or graphene. It is shown that for an isolated dielectric film the free energy and force decrease quicker with separation, as compared to the case of atom interacting with a thick plate (semispace). For metallic films some peculiar features depending on the model of a metal used are analyzed. For an atom interacting with graphene we demonstrate that at room temperature the classical regime is achieve…
We find that thin peptide films and coatings doped with metallic nanoparticles are more stable due to the role of electromagnetic fluctuations. It is shown that for the doped freestanding in vacuum peptide film the Casimir attraction becomes larger in magnitude. For dielectric substrates coated with peptide films, the nanoparticle doping leads to a wider range of film thicknesses where the Casimir pressure is attractive and to larger pressure magnitudes at the points of extremum. The doping of peptide coatings with magnetic nanoparticles preserves all the advantages of nonmagnetic ones and sim…
Precise optical properties of metals are very important for accurate prediction of the Casimir force acting between two metallic plates. Therefore we measured ellipsometrically the optical responses of Au films in a wide range of wavelengths from 0.14 mum to 33 mum. The films at various thickness were deposited at different conditions on silicon or mica substrates. Considerable variation of the frequency dependent dielectric function from sample to sample was found. Detailed analysis of the dielectric functions was performed to check the Kramers-Kronig consistency, and extract the Drude parame…
We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane ideal conductor. We employ both the Quantum Field Theory (QFT) approach, and the Lifshitz formula generalizations. The first approach turns out to be the leading order in the coupling constant of the second one. The Casimir interaction for this system appears to be rather weak but experimentally measurable. It exhibits a strong dependence on the mass of the quasi-particles in graphene.
Recent experimental data for the complete wetting behavior of pure 4He and of 3He-4He mixtures exposed to solid substrates show that there is a change of the corresponding film thicknesses L upon approaching thermodynamically the lambda-transition and the tricritical end point, respectively, which can be attributed to critical Casimir forces f_C. We calculate the scaling functions vartheta of f_C within models representing the corresponding universality classes. For the mixtures our analysis provides an understanding of the rich behavior of vartheta deduced from the experimental data and predi…
We extend our previous work on a derivative expansion for the Casimir energy, to the case of the electromagnetic field coupled to two thin, imperfect mirrors. The latter are described by means of vacuum polarization tensors localized on the mirrors. We apply the results so obtained to compute the first correction to the proximity force approximation to the static Casimir effect.
We consider the vacuum-field pressure on boundaries of a metal slab in the middle of a cavity with perfectly reflecting mirrors adopting the plasma model for the metal and paying special attention to the surface plasmon polariton contribution to the pressure. We demonstrate that, with increasing cavity length, the pressure on a thin (d<<λ_P) slab in this system decreases from the Casimir pressure F_C at zero slab-mirror distances to the non-retarded force per unit area F_nr=1.19 (d/λ_P)F_C in the case of an isolated slab. In the first case the pressure is entirely due to the photonic modes pro…
We discuss the van der Waals (Casimir) free energies and pressures of thin metallic films, consisting from one to fifteen atomic layers, with regard to the anisotropy in their dielectric properties. Both free-standing films and films deposited on a dielectric substrate are considered. The computations are performed for a Au film and a sapphire substrate. According to our results, for free-standing Au films consisting of one and three atomic layers the respective relative error arising from the use of an isotropic (bulk) dielectric permittivity is equal to 73% and 37% for the van der Waals ener…
We consider a Casimir cavity, one plate of which is a thin superconducting film. We show that when the cavity is cooled below the critical temperature for the onset of superconductivity, the sharp variation (in the far infrared) of the reflection coefficient of the film engenders a variation in the value of the Casimir energy. Even though the relative variation in the Casimir energy is very small, its magnitude can be comparable to the condensation energy of the superconducting film, and this gives rise to a number of testable effects, including a significant increase in the value of the criti…
Difference between bulk material and deposited film is shown to have an appreciable influence on the Casimir force. Analysis of the optical data on gold films unambiguously demonstrates the sample dependence: the dielectric functions of the films deposited in different conditions are different on the level that cannot be ignored in high precision prediction of the force. It is argued that the precise values of the Drude parameters are crucial for accurate evaluation of the force. The dielectric function of perfect single crystalline gold is discussed. It is used to establish the upper limit on…
We present the basic principles of non-local optics in connection with the calculation of the Casimir force between half-spaces and thin films. At currently accessible distances $L$, non-local corrections amount to about half a percent, but they increase roughly as 1/L at smaller separations. Self consistent models lead to corrections with the opposite sign as models with abrupt surfaces.
We extend a fictitious-cavity approach to calculate the Casimir effect for cavities bounded by flat anisotropic materials. We calculate the energy, force and torque in terms only of the optical coefficients of the walls of the cavity. We calculate the Casimir effect at zero and finite temperature for some simple systems. As a non trivial application, we calculate the torque between a semi-infinite anisotropic plate and an anisotropic film. We study the effect of the film thickness in the torque and find an optimal width that maximizes the torque.
In Phys. Rev. {\bf E 70}, 047102 (2004), J.R. Torgerson and S.K. Lamoreaux investigated for the first time the real-frequency spectrum of finite temperature correction to the Casimir force, for metallic plates of finite conductivity. The very interesting result of this study is that the correction from the TE mode is dominated by low frequencies, for which the dielectric description of the metal is invalid. However, their analysis of the problem, based on more appropriate low-frequency metallic boundary conditions, uses an incorrect form of boundary conditions for TE modes. We repeat their ana…
Emphasizing first the utility of the generalized Fresnel coefficients in the theory of the Casimir effect in planar cavities, we complement our previous discussion of the ordinary Casimir force on and the Casimir stress in a metal (plasma) slab in a planar cavity. We demonstrate strong dependence of the Casimir stress in a thin slab on properties of the bounding medium in the symmetric Lifshitz configuration. Contrary to this, the stress in a thick slab gradually becomes insensitive on external boundary conditions. We also consider the position dependence of the Casimir force on and stress in …
We study the Casimir energy due to a quantum real scalar field coupled to two planar, infinite, zero-width, parallel mirrors with non-homogeneous properties. These properties are represented, in the model we use, by scalar functions defined on each mirror's plane. Using the Gelfand-Yaglom's theorem, we construct a Lifshitz-like formula for the Casimir energy of such a system. Then we use it to evaluate the energy perturbatively, for the case of almost constant scalar functions, and also implementing a Derivative Expansion, under the assumption that the spatial dependence of the properties is s…
Quantum fluctuations are the key concepts of quantum mechanics. Quantum fluctuations of quantum fields induce a zero-point energy shift under spatial boundary conditions. This quantum phenomenon, called the Casimir effect, has been attracting much attention beyond the hierarchy of energy scales, ranging from elementary particle physics to condensed matter physics together with photonics. However, the application of the Casimir effect to spintronics has not yet been investigated enough, particularly to ferrimagnetic thin films, although yttrium iron garnet (YIG) is one of the best platforms for…
In a recent letter, Martin and Zagrebnov [Europhys. Lett., 73 (2006) 1] discussed the thermodynamic Casimir effect for the ideal Bose gas confined in a thin film. We point out that their findings can be expressed in terms of previous general results for the Casimir effect induced by confined critical fluctuations. This highlights the links between the Casimir effect in the contexts of critical phenomena and Bose-Einstein condensation.
We consider the out-of-thermal-equilibrium Casimir-Polder interaction between atoms of He$^*$, Na, Cs, and Rb and a cavity wall made of sapphire coated with a vanadium dioxide film which undergoes the dielectric-to-metal phase transition with increasing wall temperature. Numerical computations of the Casimir-Polder force and its gradient as the functions of atom-wall separation and wall temperature are made when the latter exceeds the temperature of the environment. The obtained results are compared with those in experiment on measuring the gradient of the Casimir-Polder force between $^{87}$R…
A recent experiment [R. A. Norte et al. Phys. Rev. Lett. {\bf 121}, 030405 (2018)] probed the variation of the Casimir force between two closely spaced thin Al films, as they transition into a superconducting state, observing a null result. We present here computations of the Casimir effect for superconductors, based on the Mattis-Bardeen formula for their optical response. We show that for the Al cavity used in the experiment the effect of the transition is over two hundred and fifty times smaller than the experimental sensitivity, in agreement with the observed null result. We demonstrate th…
We calculate the Casimir energy for scalar and gauge fields in interaction with zero-width mirrors, including quantum effects due to the matter fields inside the mirrors. We consider models where those fields are either scalar or fermionic, obtaining general expressions for the energy as a function of the vacuum field 1PI function. We also study, within the frame of a concrete model, the role of the dissipation induced by those degrees of freedom, showing that, after integration of the matter fields, the effective theory for the electromagnetic field contains modes with complex energies. As fo…
Casimir forces on suspended thin dielectric membranes covered with graphene
The Hong Kong University of Science and Technology（香港科技大学）；Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier（夏尔·库隆实验室（L2C），CNRS-蒙彼利埃大学联合研究单位5221）
Weyl semimetals are a class of topological materials that exhibit a bulk Hall effect due to time-reversal symmetry breaking. We show that for the idealized semi-infinite case, the Casimir force between two identical Weyl semimetals is repulsive at short range and attractive at long range. Considering plates of finite thickness, we can reduce the size of the long-range attraction even making it repulsive for all distances when thin enough. In the thin-film limit, we study the appearance of an attractive Casimir force at shorter distances due to the longitudinal conductivity. Magnetic field, thi…
The local Casimir energy density for a massless scalar field associated with step-function potentials in a 3+1 dimensional spherical geometry is considered. The potential is chosen to be zero except in a shell of thickness $δ$, where it has height $h$, with the constraint $hδ=1$. In the limit of zero thickness, an ideal $δ$-function shell is recovered. The behavior of the energy density as the surface of the shell is approached is studied in both the strong and weak coupling regimes. The former case corresponds to the well-known Dirichlet shell limit. New results, which shed light on the natur…
We analyze some consequences of the Casimir-type zero-point radiation pressure. These include macroscopic "vacuum" forces on a metallic layer in-between a dielectric medium and an inert ($ε(ω) = 1$) one. Ways to control the sign of these forces, based on dielectric properties of the media, are thus suggested. Finally, the large positive Casimir pressure, due to surface plasmons on thin metallic layers, is evaluated and discussed.
We study the quantum forces that act between two nearby conductors due to electronic tunneling. We derive an expression for these forces by calculating the flux of momentum arising from the overlap of evanescent electronic fields. Our result is written in terms of the electronic reflection amplitudes of the conductors and it has the same structure as Lifshitz's formula for the electromagnetically mediated Casimir forces. We evaluate the tunneling force between two semiinfinite conductors and between two thin films separated by an insulating gap. We discuss some applications of our results.
We propose the experimental scheme and present detailed theory of the optical chopper which functionality is based on the balance between the Casimir and light pressures. The proposed device consists of two atomically thin metallic mirrors forming the Fabry-Pérot microfilter. One of the mirrors is deposited on a solid cube and another one on a thinner wall subjected to bending under the influence of the attractive Casimir force and repulsive force due to the pressure of light from a continuous laser amplified in the resonator of a microfilter. The separation distance between the mirrors should…
Motivated by recent experiments with confined binary liquid mixtures near their continous demixing phase transition we study the critical behavior of a system, which belongs to the Ising universality class, for the film geometry with one planar wall chemically structured such that there is a laterally alternating adsorption preference for the species of the binary liquid mixture. By means of Monte Carlo simulations and finite-size scaling analysis we determine the critical Casimir force and the corresponding universal scaling function.
We propose a theory of the thermal Casimir interaction for multilayered test bodies coated with a graphene sheet. The reflection coefficients on such structures are expressed in terms of the components of the polarization tensor and the dielectric permittivities of material layers. The developed theory is applied to calculate the gradient of the Casimir force between an Au-coated sphere and a graphene sheet deposited on a SiO${}_2$ film covering a Si plate, which is the configuration of a recent experiment performed by means of a dynamic atomic force microscope. The theoretical results are fou…
Additional information is provided on the effect of the significant (up to 35%) reduction in the magnitude of the Casimir force between an Au-coated sphere and an indium tin oxide film which was observed after UV treatment of the latter. A striking feature of this effect is that the reduction is not accompanied with a corresponding variation of the dielectric permittivity, as confirmed by direct ellipsometry measurements. The measurement data are compared with computations using the Lifshitz theory. It is shown that the data for the untreated sample are in a very good agreement with theory tak…
