We adopt the Dirac model for quasiparticles in graphene and calculate the finite-temperature Casimir interaction between a suspended graphene layer and a parallel conducting surface. We find that at high temperature, the Casimir interaction in such system is just one-half of that for two ideal conductors separated by the same distance. In this limit, a single graphene layer behaves exactly as a Drude metal. In particular, the contribution of the TE mode is suppressed, while the contribution of the TM mode saturates at the ideal-metal value. The behavior of the Casimir interaction for intermediate temperatures and separations accessible in experiments is studied in some detail. We also find an interesting interplay between two fundamental constants of graphene physics: the fine-structure constant and the Fermi velocity.

The measurement of the lateral Casimir force between two aligned sinusoidally corrugated Au-coated surfaces has been performed in the nonadditive regime. The use of deeper corrugations also allowed us to demonstrate an asymmetry in the phase dependences of the lateral Casimir force, as predicted earlier. The measurement data are found to be in excellent agreement with the exact theoretical results computed at T = 300 K including effect of real material properties. The deviations between the exact theory and the proximity force approximation are quantified. The obtained results are topical for applications in nanomachines.The most universally known normal Casimir force 1 leads to an attraction between two closely spaced bodies directed perpendicular to their surfaces. This attraction arises due to zero-point and thermal fluctuations of the electromagnetic field. The phenomenon is important for numerous fields ranging from extradimensional physics to nanotechnology and has recently attracted considerable experimental and theoretical attentions ͑see Ref. 2͒. The most intriguing feature of the Casimir force is its nonadditivity and thus the complicated dependence on the shape of the boundary surfaces connected with diffraction effects. The nontrivial behavior of the normal Casimir force was experimentally demonstrated in the configuration of a smooth sphere above a sinusoidally corrugated plate 3 in the additive regime. Recently the normal Casimir force between an Au coated sphere and a Si plate with an array of rectangular corrugations was measured in the nonadditive regime 4 ͑where the corrugation period ⌳ is smaller than the mean separation z between the surfaces 5 ͒. The measurement data were shown to deviate from the additive theoretical results. These deviations, however, are smaller by about 50% than the prediction of Ref. 6 for ideal metals which might be explained by the interplay between nonzero skin depth and geometry effects. 4 Exact calculations performed at T = 0 taking into account the nonzero skin depth 7 favor this conjecture. In the configuration of two sinusoidally corrugated bodies ͑a sphere and a plate͒ there also arises the lateral Casimir force 8,9 which gives the possibility to actuate lateral translations in micromachines by means of the electromagnetic zero-point fluctuations. In Ref. 9 this force was measured in the additive regime ͑⌳ӷz͒. It was shown to oscillate sinusoidally as a function of the phase shift between the two corrugations.In this Rapid Communication we report measurement of the lateral Casimir force between two aligned sinusoidally corrugated surfaces of a sphere and a plate in the nonadditive regime where ⌳ ϳ z. The measurement data are found to be in excellent agreement with the exact computational results at T = 300 K taking into account real material properties. The deviation of both the experimental data and the exact theory from the prediction of the proximity force approximation ͑PFA͒ is quantified. The use here of much deeper corruga-tions than in Ref. 9 enabled the ...

We derive an exact solution for the Casimir force between two arbitrary periodic dielectric gratings and illustrate our method by applying it to two nanostructured silicon gratings. We also reproduce the Casimir force gradient measured recently [1] between a silicon grating and a gold sphere taking into account the material dependence of the force. We find good agreement between our theoretical results and the measured values both in absolute force values and the ratios between the exact force and PFA predictions.