Van der Waals and Casimir interactions near metal films

Sammanfattning: This thesis deals with van der Waals and Casimir forces near metal films. Thick, thin and strictly two-dimensional metal films will be investigated. For many applications one can model a double quantum-well structure with two strictly two-dimensional metallic sheets. The correlation energy of such structures changes when the carriers in the two sheets drift relative each other. This change in the van der Waals energy gives rise to a current drag. We found that the dragged current varies with separation as d-3.5, this is the same as the separation dependence found for the van der Waals force between thin metal films. We have used both optical data and model dielectric functions to investigate the retarded van der Waals interaction between thin and thick metal films. Usually the correct separation dependence of the van der Waals interaction can be found from simple summation of pair-interactions. Thin metallic sheets are an exception to this general rule. To find the correct separation dependence the longitudinal collective excitations must be accounted for. Using optical data and numerical methods we examined the validity of asymptotic results.The extension of the van der Waals interaction between macroscopic objects to finite temperatures is the Helmholz free energy of attraction. We have investigated the temperature dependence of the Casimir attraction between a pair of quantum wells. For many small objects found in nature, thermal effects will be a dominating source of attraction. This is also true for quantum well structures. Thermal corrections will be important already at temperatures less than 1 K. At zero temperature the retarded van der Waals energy has three separation regions. At separations of the order of the Thomas-Fermi screening length and smaller both single-particle and collective excitations contribute; in the intermediate range the collective longitudinal excitations dominate and give rise to the van der Waals forces; at large separations the collective transverse modes dominate and the result is identical to the Casimir attraction. The zero frequency part of the Helmholz free energy gives contributions at all finite temperatures. This part of the interaction will dominate at smaller and smaller separations with increasing temperatures. The interaction between thin metal films has one more conceptually interesting property. We have found that there is a possibility that the retarded van der Waals energy between two thin metal films may be larger than the corresponding non-retarded van der Waals energy. The interaction between two 20 Å gold sheets may constitute a candidate to observe this phenomenon. This is related to an unusually large relative contribution from transverse electric modes. When retardation is neglected these modes do not give any contributions at all. This anomalous effect vanishes with increasing dissipation and with increasing film thickness.In a comment on a recent calculation of the zero temperature Casimir force between imperfect conductors we corrected a few errors in the treatment of optical data. We have further investigated the temperature dependence of the Casimir force between real metal surfaces. This thesis presents result from calculations performed on both the real and imaginary frequency axis. The result is the same regardless of integration path. Using both optical data and the Drude dielectric function with dissipation included, we found a long-range high temperature asymptote in agreement with the corresponding asymptote for the interaction between quantum wells. This asymptote is in agreement with the result obtained by E. M. Lifshitz for general dielectric surfaces. It is on the other hand half as large as the result obtained by J. Schwinger and coworkers for perfect conductors. This later result has been used in comparison with experiments. It has very recently been argued that one should ignore the physical behaviour of the dielectric function in such a way as to get agreement between the high temperature asymptotes of real and ideal metals. This can be obtained if a plasma model with no dissipation is used for the dielectric response of the metals. We regard it to be a weak proof to simply claim that the correct thermal corrections to the Casimir force of a real material and an idealisation have to be identical. There is however at least one good reason why one can not simply disregard this argument. The experimental data of a recent experiment seems to agree better with this idealisation. As discussed in this thesis one should have in mind that the experimental data are found after a very large electrostatic contribution is subtracted. We have in particular found that the thermal corrections in the limit of low temperatures and small separations are substantially larger than previously assumed. We consider the disagreement between our theoretical results and the experimental ones by Lamoreaux to be intriguing and we hope that it will act as an inspiration for new experimental and theoretical efforts.In article 6 the retarded van der Waals energy of an atom between thin silver sheets was investigated. Film thickness, temperature, and retardation influence this interaction. Nienhaus et al. recently used ultra thin (∼50 Å) Ag films on a Si surface to detect hydrogen gas. Dimensionality effects are important for metallic films of this size. Our result is not relevant for that work, but could be important in other cases where atoms interact with ultra thin metal films.We have finally calculated the wetting angle as function of doping concentration for water on ln203:Sn (ITO) and determined the critical concentration for spreading. One has tried to overcome the problem of ice on car windscreens by coating the outer surface of the windshield with ITO. ITO is a both transparent and conducting material. Unfortunately, it turns out that one runs into another problem. The material wets too much. Our calculation relies on the dielectric properties of water and the doped semiconductor. We have modelled these properties.