Van der Waals (vdW) and Casimir interactions depend crucially on material properties and geometry, especially at molecular scales, and temperature can produce noticeable relative shifts in interaction characteristics. Despite this, common treatments of these interactions ignore electromagnetic retardation, atomism, or contributions of collective mechanical vibrations (phonons) to the infrared response, which can interplay with temperature in nontrivial ways. We present a theoretical framework for computing electromagnetic interactions among molecular structures, accounting for their geometry, electronic delocalization, short-range interatomic correlations, dissipation, and phonons at atomic scales, along with long-range electromagnetic interactions among themselves or in the vicinity of continuous macroscopic bodies. We find that in carbon allotropes, particularly fullerenes, carbyne wires, and graphene sheets, phonons can couple strongly with long-range electromagnetic fields, especially at mesoscopic scales (nanometers), to create delocalized phonon polaritons that significantly modify the infrared molecular response. These polaritons especially depend on the molecular dimensionality and dissipation, and in turn affect the vdW interaction free energies of these bodies above a macroscopic gold surface, producing nonmonotonic power laws and nontrivial temperature variations at nanometer separations that are within the reach of current Casimir force experiments.
In this paper we investigate the influence of ultra thin water layer (1-1.5 nm) on the van der Waals/Casimir force between gold surfaces. Adsorbed water is inevitably present on gold surfaces at ambient conditions as jump-up-to contact during adhesion experiments demonstrate. Calculations based on the Lifshitz theory give very good agreement with the experiment in absence of any water layer for surface separations d>10 nm. However, a layer of thickness h<1.5 nm is allowed by the error margin in force measurements. At shorter separations, d<10 nm, the water layer can have a strong influence as …
Van der Waals-Casimir dispersion interactions between two apposed graphene layers, a graphene layer and a substrate, and in a multilamellar graphene system are analyzed within the framework of the Lifshitz theory. This formulation hinges on a known form of the dielectric response function of an undoped or doped graphene sheet, assumed to be of a random phase approximation form. In the geometry of two apposed layers the separation dependence of the van der Waals-Casimir interaction for both types of graphene sheets is determined and compared with some well known limiting cases. In a multilamell…
We derive van der Waals-London and Casimir forces by calculating the eigenmodes of the electromagnetic field interacting with two semi-infinite bodies (two halves of space) with parallel surfaces separated by distance d. We adopt simple models for metals and dielectrics, well-known in the elementary theory of dispersion. In the non-retarded (Coulomb) limit we get a d^{-3}-force (van der Waals-London force), arising from the zero-point energy (vacuum fluctuations) of the surface plasmon modes. When retardation is included we obtain a d^{-4}-(Casimir) force, arising from the zero-point energy of…
Forces induced by quantum fluctuations of electromagnetic field control adhesion phenomena between rough solids when the bodies are separated by distances ~10nm. However, this distance range remains largely unexplored experimentally in contrast with the shorter (van der Waals forces) or the longer (Casimir forces) separations. The reason for this is the pull-in instability of the systems with the elastic suspension that poses a formidable limitation. In this paper we propose a genuine experimental configuration that does not suffer from the short distance instability. The method is based on ad…
In order to understand why carbon dioxide (CO$_2$) and methane (CH$_4$) molecules interact differently with surfaces, we investigate the Casimir-Polder energy of a linearly polarizable CO$_2$ molecule and an isotropically polarizable CH$_4$ molecule in front of an atomically thin gold film and an amorphous silica slab. We quantitatively analyze how the anisotropy in the polarizability of the molecule influences the van der Waals contribution to the binding energy of the molecule.
It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic potentials of the damped harmonic oscillator bilinearly coupled to the environment. An extended model for a damped oscillator is suggested along the lines of the general theory of Casimir and van der Waals forces, and the corresponding thermodynamic quantities obtained. While the original model involves a heat bath consisting of a large number of free oscillators having infinitesimal damping functions, the extended model allows any generally admissible freq…
We present an approach for computing long-range van der Waals (vdW) interactions between complex molecular systems and arbitrarily shaped macroscopic bodies, melding atomistic treatments of electronic fluctuations based on density functional theory in the former, with continuum descriptions of strongly shape-dependent electromagnetic fields in the latter, thus capturing many-body and multiple scattering effects to all orders. Such a theory is especially important when considering vdW interactions at mesoscopic scales, i.e. between molecules and structured surfaces with features on the scale of…
The thermal free energy and pressure of dispersion interaction between two graphene sheets described by the Dirac model are calculated using the Lifshitz formula with reflection coefficients expressed via the polarization tensor. The obtained results for a pristine graphene are found to be in agreement with computations using Coulomb coupling between density fluctuations. For a graphene with nonzero mass gap parameter a qualitatively different behavior for the free energy and pressure is obtained. The Lifshitz formula with reflection coefficients expressed via the polarization tensor is used a…
We study the classical thermal component of Casimir, or van der Waals, forces between point particles with highly anharmonic dipole Hamiltonians when they are subjected to an external electric field. Using a model for which the individual dipole moments saturate in a strong field (a model that mimics the charges in a neutral, perfectly conducting sphere), we find that the resulting Casimir force depends strongly on the strength of the field, as demonstrated by analytical results. For a certain angle between external field and center to center axis, the fluctuation force can be tuned and suppre…
To investigate the role of long-range van der Waals interactions in static friction, we derive an analytic expression for the coefficient of static friction $μ_s$ between two thin layers of polarizable materials under zero load. For simplicity, we model the surface roughness with sinusoidal corrugations and calculate the interaction energy perturbatively up to the second order in corrugation amplitude. The ratio of corresponding maximum lateral Casimir force to normal Casimir force is defined as the coefficient of static friction, which is found to be independent of the dielectric properties o…
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 present vibrational properties of Franckeite, which is a naturally occurring van der Waals heterostructure consisting of two different semiconducting layers. Franckeite is a complex layered crystal composed of alternating SnS$_2$ like pseudohexagonal and PbS-like pseudotetragonal layers stacked on top of each other, providing a unique platform to study vibrational properties and thermal transport across layers with mass density and phonon mismatches. By using micro-Raman spectroscopy and first-principles Raman simulations, we found that the PbS-like pseudotetragonal structure is mostly comp…
The non-retarded Casimir interaction (van der Waals interaction) between two free standing graphene sheets as well as between a graphene sheet and a substrate is determined. An exact analytical expression is given for the dielectric function of graphene along the imaginary frequency axis within the random phase approximation for arbitrary frequency, wave vector, and doping.
We have investigated the vibrational properties of van der Waals heterostructures of monolayer transition metal dichalcogenides (TMDs), specifically MoS2/WSe2 and MoSe2/MoS2 heterobilayers as well as twisted MoS2 bilayers, by means of ultralow-frequency Raman spectroscopy. We discovered Raman features (at 30 ~ 40 cm-1) that arise from the layer-breathing mode (LBM) vibrations between the two incommensurate TMD monolayers in these structures. The LBM Raman intensity correlates strongly with the suppression of photoluminescence that arises from interlayer charge transfer. The LBM is generated on…
In this article, we rigorously analyze the effects of the dispersion forces (Casimir and van der Waals forces) on a nano-optomechanical device based on a silicon waveguide and a silicon dioxide substrate, surrounded by air and driven by optical forces. The dispersion forces are calculated using a modified Lifshitz theory, in order to take into account the device thickness and material s dielectric permittivities, which are obtained from experimental optical data and validated by means of a rigorous 3D FDTD simulation. We also take into account the mechanical nonlinearity of the waveguide, whic…
Most often in chemical physics, long range van der Waals surface interactions are approximated by the exact asymptotic result at vanishing distance, the well known additive approximation of London dispersion forces due to Hamaker. However, the description of retardation effects that is known since the time of Casimir is completely neglected for lack of a tractable expression. Here we show that it is possible to describe surface van der Waals forces at arbitrary distances in one single simple equation. The result captures the long sought crossover from non-retarded (London) to retarded (Casimir…
We derive a first--principles method of determining the van der Waals or Casimir pressure in a dissipative and dispersive planar multilayered system by calculating the Maxwell stress tensor in a fictitious layer of vacuum, that is eventually made to vanish, introduced in the structure. This is illustrated by calculating the van der Waals pressure in a thin film with dissipative properties embedded between two semi--infinite media.
We derive a general procedure for finding the electromagnetic normal modes in layered structures. We apply this procedure to planar, spherical and cylindrical structures. These normal modes are important in a variety of applications. They are the only input needed in calculations of Casimir interactions. We present explicit expression for the condition for modes and Casimir energy for a large number of specific geometries. The layers are allowed to be two-dimensional so graphene and graphene-like sheets as well as two-dimensional electron gases can be handled within the formalism. Also forces …
We reveal stacking-induced strong coupling between atomic motion and interlayer excitons through photocurrent measurements of WSe$_2$/MoSe$_2$ heterojunction photodiodes. Strong coupling manifests as pronounced periodic sidebands in the photocurrent spectrum in frequency windows close to the interlayer exciton resonances. The sidebands, which repeat over large swathes of the interlayer exciton photocurrent spectrum, occur in energy increments corresponding directly to a prominent vibrational mode of the heterojunction. Such periodic patterns, together with interlayer photoconductance oscillati…
We present an approach for modeling nanoscale wetting and dewetting of liquid surfaces that exploits recently developed, sophisticated techniques for computing van der Waals (vdW) or (more generally) Casimir forces in arbitrary geometries. We solve the variational formulation of the Young--Laplace equation to predict the equilibrium shapes of fluid--vacuum interfaces near solid gratings and show that the non-additivity of vdW interactions can have a significant impact on the shape and wetting properties of the liquid surface, leading to very different surface profiles and wetting transitions c…
The Casimir-Polder interaction between an atom and a multilayered system composed of infinitely thin planes is considered using the zeta-function regularization approach with summation of the zero-point energies. As a prototype material, each plane is represented by a graphene sheet whose optical response is described by a constant conductivity or Drude-Lorentz model conductivity. Asymptotic expressions for various separations are derived and compared to numerical calculations. We distinguish between large atom/plane limit, where retardation effects are prominent, and small atom/plane limit, w…
The phonon Casimir effect describes the phonon-mediated interaction between defects in condensed-matter systems. Using the path-integral formalism, we derive a general method for calculating the Helmholtz free energy due to vibrational modes in systems of arbitrary dimensionality and composition. Our results make it possible to extract the defect interaction energy at any temperature for various defect configurations. We demonstrate our approach in action by performing numerical calculations for mono- and diatomic chains, as well as a diatomic molecule, at zero and finite temperatures and vali…
We investigate the error made by the pairwise summation (PWS) approximation in three geometries where the exact formula for the Casimir interaction is known: atom-slab, slab-slab and sphere-slab configurations. For each case the interactions are calculated analytically by summing the van der Waals interactions between the two objects. We show that the PWS result is incorrect even for an infinitely thin slab in the atom-slab configuration, because of local field effects, unless the material is infinitely dilute. In the experimentally relevant case of dielectric materials, in all considered geom…
We present a combined experimental and theoretical study of the surface vibrational modes of the topological insulator Bi$_2$Te$_3$. Using high-resolution helium-3 spin-echo spectroscopy we are able to resolve the acoustic phonon modes of Bi$_2$Te$_3$(111). The low energy region of the lattice vibrations is mainly dominated by the Rayleigh mode which has been claimed to be absent in previous experimental studies. The appearance of the Rayleigh mode is consistent with previous bulk lattice dynamics studies as well as theoretical predictions of the surface phonon modes. Density functional pertur…
We consider the van der Waals energy of an atom near the infinitely thin sphere with finite conductivity which model the fullerene. We put the sphere into spherical cavity inside the infinite dielectric media, then calculate the energy of vacuum fluctuations in framework of the zeta-function approach. The energy for a single atom is obtained from this expression by consideration of the rare media. In the limit of the infinite radius of the sphere the Casimir-Polder expression for an atom and plate is recovered. For finite radius of sphere the energy of an atom monotonously falls down as $d^{-3…
In inhomogeneous dielectric media the divergence of the electromagnetic stress is related to the gradients of \varepsilon and μ, which is a consequence of Maxwell's equations. Investigating spherically symmetric media we show that this seemingly universal relationship is violated for electromagnetic vacuum forces such as the generalized van der Waals and Casimir forces. The stress needs to acquire an additional anomalous pressure. The anomaly is a result of renormalization, the need to subtract infinities in the stress for getting a finite, physical force. The anomalous pressure appears in the…
We report first-principles calculations of the structural and vibrational properties of the synthesized two-dimensional van der Waals heterostructures formed by single-layers dichalcogenides MoSe2 and WSe2. We show that, when combining these systems in a periodic two-dimensional heterostructures, the intrinsic phonon characteristics of the free-standing constituents are to a large extent preserved but, furthermore, exhibit shear and breathing phonon modes that are not present in the individual building blocks. These peculiar modes depend strongly on the weak vdW forces and has a great contibut…
We study the effect of salts on the thickness of wetting films on melting ice and interactions acting on CO$_2$ bubble near ice-water and vapor-water interfaces. Governing mechanisms are the Lifshitz and the double-layer interactions in the respective three-layer geometries. We demonstrate that the latter depend on the Casimir--Polder interaction of the salt ions dissolved in water with the respective ice, vapour and CO$_2$ interfaces, as calculated using different models for their effective polarizability in water. Significant variation in the predicted thickness of the equilibrium water film…
Nanoscale surface forces such as Casimir and the van der Waals forces can have a significant influence on fabrication, handling and assembly processes as well as the performance of micro and nano devices. In this paper, the investigation and the calculation of the Casimir force between a graphene sheet and a ferromagnetic metal substrate in a vacuum are presented. The reflection coefficients of graphene are graphene-conductivity dependent, and the conductivity of graphene is described by the Kubo formalism. There is an effect of magnetic properties of the metal on the Casimir interaction. The …
