Marco Govoni, Carlo Calandra, Andrea Benassi
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.
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The Casimir effect is investigated in cylindrical and toroidal carbon nanotubes within the framework of the Dirac-like model for the electronic states. The topological Casimir energy is positive for metallic cylindrical nanotubes and is negative for semiconducting ones. The toroidal compactification of a cylindrical nanotube along its axis increases the Casimir energy for metallic-type (periodic) boundary conditions along its axis and decreases the Casimir energy for the semiconducting-type compactifications. For finite length metallic nanotubes the Casimir forces acting on the tube edges are …
Properties of metallic films in precise calculation of the Casimir force
沉积的金膜的光学性质进行了讨论与卡西米尔力预测。与散装材料预测相比，薄膜中的空隙和晶界上的电子散射在2%的水平上降低了小分离处的力。由于薄膜的多晶结构的补丁电位的贡献被证明是小的现有的Casimir力实验。
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 …
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…
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 report development of a high-sensitivity torsion balance to measure the thermal Casimir force. Special emphasis is placed on experimental investigations of a possible surface electric force originating from surface patch potentials that have been recently noticed by several experimental groups. By gaining a proper understanding of the actual contribution of the surface electric force in real materials, we aim to undertake precision force measurements to resolve the Casimir force at finite temperature in real metals, as well as in other semiconducting materials, such as graphene.
Casimir effect for thin films from imperfect materials
提出了一种研究薄膜材料与量子电动力学场相互作用的方法。利用量子电动力学的主要原理（局部性，规范不变性，重整化），我们构建了一个单一的模型Casimir类似的现象附近产生的距离远大于康普顿波长的电子的狄拉克场的波动是不必要的膜边界。在该模型中，薄膜由集中在二维表面上的奇异背景场表示。薄膜材料的所有性质都用一个无量纲参数来描述。对于两个平行的平面膜，我们计算的光子传播和Casimir力，这似乎是依赖于薄膜材料，可以是吸引力和排斥力。我们还考虑了平面薄膜与点电荷和直线电流的相互作用。在这里，除了通常的经典电动力学的结果，该模型预测出现异常的电场和磁场。
Non-local thin films in Casimir force calculations
计算了薄金属涂层平板间的Casimir力。薄膜用空间色散（非局部）介电函数来描述。对于薄膜的非局部效应是更相关的比半空间。然而，它表明，即使膜厚度小于平均自由程的电子，Casimir力的本地和非本地计算之间的差异是百分之零点几的顺序。因此，在目前的实验精度和分离范围内，金属薄膜的局部描述是足够的。
Casimir force calculations near the insulator-conductor transition in gold thin films
我们目前的理论计算的Casimir力的金薄膜附近的绝缘体-导体的转变，已观察到的实验。Au薄膜的介电函数用Drude-Smith模型描述。模型的介电函数，如弛豫时间，等离子体频率和背散射常数的参数依赖于膜的厚度。Casimir力随着膜厚度减小而减小，直到其达到最小值，之后力再次增大。该力的最小值与临界膜厚一致，在该临界膜厚处发生渗流导体-绝缘体。
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 imperfect termination of static electric fields at semiconducting surfaces has been long known in solid state and transistor physics. We show that the imperfect shielding leads to an offset in the distance between two surfaces as determined by electrostatic force measurements. The effect exists even in the case of good conductors (metals) albeit much reduced.
Frequency-dependent Drude damping in Casimir force calculations
采用Drude模型和频率相关阻尼函数计算了Au薄膜之间的Casimir力。模型参数由Au薄膜的实验数据得到。两种情况下被认为是退火和nonannealed薄膜，具有不同的阻尼功能。与使用具有恒定阻尼参数的Drude模型的计算相比，我们观察到Casimir力的几个百分点的变化。这种行为仅在不超过300 $Å$厚的膜中观察到。
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 …
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…
The Casimir free energy of peptide films on a silicon substrate: Impact of dielectric-to-metal transition in silicon and nanoparticles in peptide
研究硅衬底的介电-金属相变及肽膜中纳米颗粒对卡西米尔自由能的影响，明确了肽膜厚度临界值的变化规律，为其在有机电子和生物医学的应用提供理论依据。
Comment on "Anomalous temperature dependence of the Casimir force for thin metal films" [arXiv:0712.1395]
最近，A。Yampol'skii，S. Savel'ev，Z. A. Mayselis，S. S. Apostolov和F.海苔[Phys. Rev. Lett.，101，096803（2008），arXiv：0712.1395]声称，由Drude模型描述的薄金属膜和理想金属半空间之间的Casimir力可以随温度降低，而对于体样品，Casimir力随温度增加。在此基础上，提出了薄膜与块状理想金属之间Casimir力大小随温度变化的实验观测结果。我们表明，与作者所声称的相反，Casimir力的大小随温度的降低在一个宽的温度区域的散装样品所描述的德鲁德模型。这种减少被证明是远远大于一个薄膜，它已经被实验排除。
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…
The Low-Frequency Character of the Thermal Correction to the Casimir Force between Metallic Films
Casimir力的有限温度修正的频谱可以通过使用有限传导率金属板的Lifshitz形式来确定。我们表明，TE电磁模式的校正是由频率如此之低，板不能被建模为理想的电磁波。我们还解决了有关的问题，在金属导体的表面和内的电磁场的行为，并claculate使用适当的低频金属边界条件的表面模式。我们的结果带来的tehrmal修正到协议与先前获得的实验结果。
The Effect of Epsilon-Near-Zero (ENZ) Modes on the Casimir Interaction between Ultrathin Films
首次从实频率力分布角度研究超薄膜间 Casimir 相互作用，发现 ENZ 模式产生显著排斥贡献且与间距无关，揭示了其在纳米机械系统中的工程化潜力。
The Low-Frequency Character of the Thermal Correction to the Casimir Force between Metallic Films
Casimir力的有限温度修正的频谱可由有限电导率金属板的Lifshitz公式确定。我们表明，校正的$TE$电磁模式是占主导地位的频率如此之低，板不能被建模为理想的电磁波。我们还解决了与电磁场在表面和金属导体内的行为有关的问题，并使用适当的低频金属边界条件计算表面模式。我们的结果使热修正与先前获得的实验结果一致。我们提出了一系列的测量方法来检验我们分析的准确性。
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 …
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 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.
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…
Optical properties of gold films and the Casimir force
金属的精确光学性质对于精确预测作用在两金属板之间的Casimir力是非常重要的。因此，我们椭圆偏振测量的Au膜的光学响应在很宽的波长范围从0.14妈妈到33妈妈。在不同条件下在硅或云母衬底上沉积不同厚度的膜。对薄膜的介电函数进行了详细的分析，验证了Kramers-Kronig一致性，并提取了薄膜的Drude参数。发现等离子体频率在6.8 ~ 8.4eV范围内变化。这种变化与薄膜密度有关。X射线反射率测量定性支持这一结论。卡西米尔力的评价对应于我们的样品的介电函数，通常用于精确预测的力。我们的膜的力被发现在板之间的100 nm的距离处小5-14%。光学数据中的噪声对1%以内的力变化负责。结果表明，预测金属间Casimir力的精度优于10%，必须基于从可见光到中红外范围内测量的材料光学响应。
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…
Efficient Reduction of Casimir Forces by Self-assembled Bio-molecular Thin Films
本研究实验发现自组装生物分子薄膜可将平板与球体间的 Casimir 力减小达14%，并通过 Lifshitz 理论验证其机制，为解决 MEMS 微型化中的粘附问题提供了新途径。
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…
Towards measuring variations of Casimir energy by a superconducting cavity
我们考虑一个Casimir腔，其中的一个板是一个薄的超导膜。我们表明，当腔冷却到超导性的开始低于临界温度，急剧变化（在远红外）的反射系数的膜引起的卡西米尔能量的值的变化。尽管卡西米尔能量的相对变化非常小，但其大小可以与超导膜的凝聚能相当，并且这引起许多可测试的效应，包括破坏膜的超导性所需的临界磁场值的显著增加。因此，理论上的基础是为有史以来第一次旨在测量卡西米尔能量本身的变化的实验做准备。
Observation of the skin-depth effect on the Casimir force between metallic surfaces
我们对金属板和涂有不同厚度金属膜的透明球之间的卡西米尔力进行了比较测量。我们已经观察到，如果涂层的厚度小于主要有助于相互作用的电磁模式的趋肤深度，则力显著小于用厚块状膜测量的力。我们的研究结果提供了第一个直接证据的趋肤深度效应的Casimir力之间的金属表面。
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 …
Critical Casimir Effect in superfluid wetting films
最近对纯~ 4 He和~ 3 He-~ 4 He混合物在固体基底上的完全润湿行为的实验数据表明，在分别接近临界转变点和三临界点时，相应的膜厚L会发生变化，这可归因于临界Casimir力fC。我们计算的标度函数vartheta的f_C内的模型表示相应的普适类。对于混合物，我们的分析提供了一个丰富的行为vartheta从实验数据推导出的理解和预测的三临界点和纯4 He的三临界点之间的交叉行为，这是连接的临界点线。在润湿膜内形成“软模式”相，实验观察到在三临界点以下f_C出现明显的最大值。在三临界点附近，我们发现vartheta的主导行为的对数修正~L^（-3）（ln L）^（1/2）主导了背景色散力的贡献。
Proposal to measure the Casimir Effect Across the Superconducting Transition
本文提出利用平行磁场在厚膜中诱导一级超导转变，通过周期性调制磁场使卡西米尔力产生可检测的调制，从而首次实验验证卡西米尔效应与超导的耦合。
Casimir-like tunneling-induced electronic forces
我们研究了由于电子隧穿作用在两个相邻导体之间的量子力。我们推导出一个表达式，这些部队通过计算所产生的倏逝电子场的重叠的动量通量。我们的结果是书面的电子反射振幅的导体，它具有相同的结构作为Lifshitz的电磁介导的Casimir力的公式。我们计算了两个半无限导体之间和两个由绝缘间隙隔开的薄膜之间的隧穿力。我们讨论了我们的结果的一些应用。
Sample dependence of the Casimir force
体材料和沉积膜之间的差异示出有一个明显的影响卡西米尔力。对金膜的光学数据的分析明确地表明了样品依赖性：在不同条件下沉积的膜的介电函数在力的高精度预测中不可忽略的水平上是不同的。有人认为，德鲁德参数的精确值是至关重要的准确评估的力量。本文讨论了金单晶的介电函数。它用于确定力的绝对值的上限。结果表明，薄膜之间的作用力小于体样品之间的作用力，这主要是由于薄膜中存在空隙和晶界上的电子散射。在最精确的实验中，对于最小的分离，力的最小减少估计为2%。其他样品效应可以进一步减小力，但预计校正小于1%。
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.
We describe an isoelectronic differential apparatus designed to observe the influence on the Casimir force of the Mott-Anderson metal-insulator transition in doped semiconductors. Alternative theories of dispersion forces lead to different predictions for this effect. The investigation of this problem by standard apparatus, based on absolute measurements of the Casimir force, is very difficult because the effect is small in the region of sub-micron separations, where the Casimir force can be measured precisely. The differential apparatus described here is immune by design to several sources of…
Comment on " Low-frequency character of the Casimir force between metallic films"
在Phys. Rev. { \bf E 70}，047102（2004），J.R. Torgerson和S.K. Lamoreaux调查的第一次真正的频谱的有限温度修正卡西米尔力，金属板的有限导电性。这项研究的一个非常有趣的结果是，TE模式的校正主要是由低频，金属的介电描述是无效的。然而，他们的问题分析，基于更合适的低频金属边界条件，使用了不正确的TE模式的边界条件形式。我们重复他们的分析，使用正确的边界条件。我们的计算证实了他们最重要的结果：相反的电介质模型的结果，热TE模式校正导致板之间的TE模式吸引力的增加。修正的幅度比他们引用的数值大20倍左右。
Relation between the thermodynamic Casimir effect in Bose-gas slabs and critical Casimir forces
在最近的一封信中，马丁和扎格雷布诺夫[Europhys。信件：73（2006）1]讨论了限制在薄膜中的理想玻色气体的热力学Casimir效应。我们指出，他们的研究结果可以表示在以前的一般结果的Casimir效应引起的限制临界波动。这突出了在临界现象和玻色-爱因斯坦凝聚的上下文中的卡西米尔效应之间的联系。
Spatial dispersion in Casimir forces: A brief review
本文介绍了半空间与薄膜之间Casimir力的计算中的非局域光学的基本原理。在目前可达的距离$L$，非局部校正量约为0.5%，但它们在较小的间隔下大致增加1/L。自洽模型导致与突变表面的模型相反的符号的校正。
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…
Machine-learning-assisted material and geometry characterization from Casimir force measurement
本文利用机器学习方法从Casimir力测量中推断纳米薄膜的厚度和介电常数，展示了量子真空波动作为宽带电磁源在材料表征中的应用潜力。
Quantum theory predicts the existence of the Casimir force between macroscopic bodies, due to the zero-point energy of electromagnetic field modes around them. This quantum fluctuation-induced force has been experimentally observed for metallic and semiconducting bodies, although the measurements to date have been unable to clearly settle the question of the correct low-frequency form of the dielectric constant dispersion (the Drude model or the plasma model) to be used for calculating the Casimir forces. At finite temperature a thermal Casimir force, due to thermal, rather than quantum, fluct…
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.
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