Demonstration of an Unusual Thermal Effect in the Casimir Force from Graphene.

We report precision measurements of the gradient of the Casimir force between an Au-coated sphere and graphene sheet deposited on a silica plate. The measurement data are compared with exact theory using the polarization tensor found in the framework of the Dirac model including effects of the nonzero chemical potential and energy gap of the graphene sample with no fitting parameters. The very good agreement between experiment and theory demonstrates the unusually big thermal effect at separations below 1 µm which has never been observed for conventional 3D materials. Thus, it is confirmed experimentally that for graphene the effective temperature is determined by the Fermi velocity rather than by the speed of light.

Reflectance of graphene-coated dielectric plates in the framework of Dirac model: joint action of energy gap and chemical potential.

We investigate the reflectance of a dielectric plate coated with a graphene sheet which possesses the nonzero energy gap and chemical potential at any temperature. The general formalism for the reflectance using the polarization tensor is presented in the framework of Dirac model. It allows calculation of the reflectivity properties for any material plate coated with real graphene sheet on the basis of first principles of quantum electrodynamics. Numerical computations of the reflectance are performed for the graphene-coated SiO2 plate at room, liquid-nitrogen, and liquid-helium temperatures. We demonstrate that there is a nontrivial interplay between the chemical potential, energy gap, frequency, and temperature in their joint action on the reflectance of a graphene-coated plate. Specifically, it is shown that at the fixed frequency of an incident light an increase of the chemical potential and the energy gap affect the reflectance in opposite directions by increasing and decreasing it, respectively. According to our results, the reflectance approaches unity at sufficiently low frequencies and drops to that of an uncoated plate at high frequencies for any values of the chemical potential and energy gap. The impact of temperature on the reflectance is found to be more pronounced for graphene coatings with smaller chemical potentials. The obtained results could be applied for optimization of optical detectors and other devices exploiting graphene coatings.

Fluctuation-induced free energy of thin peptide films.

We apply the Lifshitz theory of dispersion forces to find a contribution to the free energy of peptide films that is caused by the zero-point and thermal fluctuations of the electromagnetic field. For this purpose, using available information about the imaginary parts of the dielectric permittivity of peptides, an analytic representation for permittivity of a typical peptide along the imaginary frequency axis is devised. Numerical computations of the fluctuation-induced free energy are performed at room temperature for freestanding peptide films containing different fractions of water, and for similar films deposited on dielectric (SiO_{2}) and metallic (Au) substrates. It is shown that the free energy of a freestanding peptide film is negative and thus contributes to its stability. The magnitude of the free energy increases with increasing fraction of water and decreases with increasing thickness of a film. For peptide films deposited on a dielectric substrate, the free energy is nonmonotonous. It is negative for films thicker than 100nm, reaches the maximum value at some film thickness, but vanishes and changes its sign for films thinner than 100nm. The fluctuation-induced free energy of peptide films deposited on metallic substrate is found to be positive, which makes films less stable. In all three cases, simple analytic expressions for the free energy of sufficiently thick films are found. The obtained results may be useful to attain film stability in the next generation of organic microdevices with further reduced dimensions.

Nonperturbative theory of atom-surface interaction: corrections at short separations.

The nonperturbative expressions for the free energy and force of interaction between a ground-state atom and a real-material surface at any temperature are presented. The transition to the Matsubara representation is performed, whereupon the comparison is made with the commonly used perturbative results based on the standard Lifshitz theory. It is shown that the Lifshitz formulas for the free energy and force of an atom-surface interaction follow from the nonperturbative ones in the lowest order of the small parameter. Numerical computations of the free energy and force for the atoms of He[Formula: see text] and Na interacting with a surface of an Au plate have been performed using the frequency-dependent dielectric permittivity of Au and highly accurate dynamic atomic polarizabilities in the framework of both the nonperturbative and perturbative theories. According to our results, the maximum deviations between the two theories are reached at the shortest atom-surface separations of about 1 nm. Simple analytic expressions for the atom-surface free energy are derived in the classical limit and for an ideal-metal plane. In the lowest order of the small parameter, they are found in agreement with the perturbative ones following from the standard Lifshitz theory. Possible applications of the obtained results in the theory of van der Waals adsorption are discussed.

Casimir free energy of dielectric films: classical limit, low-temperature behavior and control.

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 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 is found. According to our results, the Casimir entropy goes to zero when the temperature vanishes if the calculation approach with neglected dc conductivity of a film is employed. If the dc conductivity is taken into account, the Casimir entropy takes the positive value at zero temperature, depending on the parameters of a film, i.e. the Nernst heat theorem is violated. By considering the Casimir free energy of SiO2 and Al2O3 films deposited on a Au plate in the framework of two calculation approaches, we argue that physically correct values are obtained by disregarding the role of dc conductivity. A comparison with the well known results for the configuration of two parallel plates is made. Finally, we compute the Casimir free energy of SiO2, Al2O3 and Ge films deposited on high-resistivity Si plates of different thicknesses and demonstrate that it can be positive, negative and equal to zero. The effect of illumination of a Si plate with laser light is considered. Possible applications of the obtained results to thin films used in microelectronics are discussed.

Comment on "Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors".

Recently Guérout et al. [Phys. Rev. E 93, 022108 (2016)1539-375510.1103/PhysRevE.93.022108] advocated that the lossless plasma model has to be redefined as the limit of the Drude model when the relaxation parameter goes to zero. It was claimed that the previously used plasma model cannot correctly describe the Casimir pressure between two plates made of both nonmagnetic and magnetic metals and has to be replaced with the redefined one. We show that the suggested redefinition does not satisfy necessary physical requirements imposed on the dielectric permittivity. We also present a plausible explanation for the fact that the lossless plasma model describes the Casimir pressure correctly even though it does not match the optical and electrical properties of metals.

Casimir entropy for magnetodielectrics.

We find the analytic expressions for the Casimir free energy, entropy and pressure at low temperature in the configuration of two parallel plates made of magnetodielectic material. The cases of constant and frequency-dependent dielectic permittivity and magnetic permeability of the plates are considered. Special attention is paid to the account of dc conductivity. It is shown that in the case of finite static dielectric permittivity and magnetic permeability the Nernst heat theorem for the Casimir entropy is satisfied. If the dc conductivity is taken into account, the Casimir entropy goes to a positive nonzero limit depending on the parameters of a system when the temperature vanishes, i.e. the Nernst theorem is violated. The experimental situation is also discussed.

Demonstration of the Casimir force between ferromagnetic surfaces of a Ni-coated sphere and a Ni-coated plate.

We demonstrate the Casimir interaction between two ferromagnetic boundary surfaces using the dynamic atomic force microscope. The experimental data are found to be in excellent agreement with the predictions of the Lifshitz theory for magnetic boundary surfaces combined with the plasma model approach. It is shown that for magnetic materials the role of hypothetical patch potentials is opposite to that required for reconciliation of the data with the Drude model.

How to modify the van der Waals and Casimir forces without change of the dielectric permittivity.

We propose a new experiment on the measurement of the Casimir force and its gradient between a Au-coated sphere and two different plates made of doped semiconductors. The concentrations of charge carriers in the plates are chosen slightly below and above the critical density at which the Mott-Anderson insulator-metal transition occurs. We calculate changes in the Casimir force and the Casimir pressure due to the insulator-metal transition using the standard Lifshitz theory and the phenomenological approach neglecting the contribution of free charge carriers in the dielectric permittivity of insulator materials (this approach was recently supported by the measurement data of several experiments). It is demonstrated that for the special selection of semiconductor materials (S- or Se-doped Si, B-doped diamond) the calculation results using the two theoretical approaches differ significantly and the predicted effects are easily detectable using the existing laboratory setups. In the case that the prediction of the phenomenological approach is confirmed, this would open opportunities to modify the van der Waals and Casimir forces with almost no change of room temperature dielectric permittivity.

Reduction of the Casimir force from indium tin oxide film by UV treatment.

A significant decrease in the magnitude of the Casimir force (from 21% to 35%) was observed after an indium tin oxide sample interacting with an Au sphere was subjected to the UV treatment. Measurements were performed by using an atomic force microscope in high vacuum. The experimental results are compared with theory and a hypothetical explanation for the observed phenomenon is proposed.

Comment on "Analytical and numerical verification of the Nernst theorem for metals".

Recently, Høye, Brevik, Ellingsen, and Aarseth [Phys. Rev. E 75, 051127 (2007)] claimed that the use of the Drude dielectric function leads to zero Casimir entropy at zero temperature in accordance with Nernst's theorem. We demonstrate that their proof is not applicable to metals with perfect crystal lattices having no impurities. Thus there is no contradiction with previous results in the literature proving that the Drude dielectric function violates the Nernst theorem for the Casimir entropy in the case of perfect crystal lattices. We also indicate that the approximation of temperature independent relaxation frequency used in the paper leads to incorrect values of numerical coefficients in the obtained asymptotic expressions for metals with impurities.

Demonstration of optically modulated dispersion forces.

We report the first experiment on the optical modulation of dispersion forces through a change of the carrier density in a Si membrane. For this purpose a high-vacuum based atomic force microscope and excitation light pulses from an Ar laser are used. The experimental results are compared with two theoretical models. The modulation of the dispersion force will find applications in optomechanical micromachines.

Demonstration of the difference in the Casimir force for samples with different charge-carrier densities.

A measurement of the Casimir force between a gold coated sphere and two Si plates of different carrier densities is performed using a high vacuum based atomic force microscope. The results are compared with the Lifshitz theory and good agreement is found. Our experiment demonstrates that by changing the carrier density of the semiconductor plate by several orders of magnitude it is possible to modify the Casimir interaction. This result may find applications in nanotechnology.

Comment on "temperature dependence of the Casimir effect".

Recently, Brevik [Phys. Rev. E, 71, 056101 (2005)] adduced arguments against the traditional approach to the thermal Casimir force between real metals and in favor of one of the alternative approaches. The latter assume zero contribution from the transverse electric mode at zero frequency in qualitative disagreement with unity as given by the thermal quantum field theory for ideal metals. Those authors claim that their approach is consistent with experiments as well as with thermodynamics. We demonstrate that these conclusions are incorrect. We show specifically that their results are contradicted by four recent experiments and also violate the third law of thermodynamics (the Nernst heat theorem).

New features of the thermal Casimir force at small separations.

The difference of the thermal Casimir forces at different temperatures between real metals is shown to increase with a decrease of the separation distance. This opens new opportunities for the demonstration of the thermal dependence of the Casimir force. Both configurations of two parallel plates and a sphere above a plate are considered. Different approaches to the theoretical description of the thermal Casimir force are shown to lead to different measurable predictions.

Demonstration of the lateral casimir force.

The lateral Casimir force between a sinusoidally corrugated gold coated plate and large sphere was measured for surface separations between 0.2 to 0.3 microm using an atomic force microscope. The measured force shows the required periodicity corresponding to the corrugations. It also exhibits the necessary inverse fourth power distance dependence. The obtained results are shown to be in good agreement with a complete theory taking into account the imperfectness of the boundary metal. This demonstration opens new opportunities for the use of the Casimir effect for lateral translation in microelectromechanical systems.