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Van der Waals and Casimir interactions near metal films
Linköping University, Department of Physics, Measurement Technology, Biology and Chemistry. Linköping University, The Institute of Technology.
2000 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Linköping: Linköping University , 2000. , p. 52
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 630
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:liu:diva-183663Libris ID: 7624524ISBN: 9172197196 (print)OAI: oai:DiVA.org:liu-183663DiVA, id: diva2:1645241
Public defence
2000-06-06, Planck, Fysikhuset, Linköpings universitet, Linköping, 10:15
Opponent
Note

All or some of the partial works included in the dissertation are not registered in DIVA and therefore not linked in this post.

Available from: 2022-03-16 Created: 2022-03-16 Last updated: 2022-03-16Bibliographically approved
List of papers
1. Temperature effects on the Casimir attraction between a pair of quantum wells
Open this publication in new window or tab >>Temperature effects on the Casimir attraction between a pair of quantum wells
2000 (English)In: Microelectronic Engineering, ISSN 0167-9317, E-ISSN 1873-5568, Vol. 51, p. 287-297Article in journal (Refereed) Published
Abstract [en]

We present calculations of the free energy of attraction between two quantum wells in which the wells are treated as strictly two-dimensional metallic sheets. The van der Waals force exhibits fractional separation dependence in this system. This is in contrast to the usual integer separation dependence. We have performed numerical calculations at different temperatures and with different carrier densities. Except at very low temperatures thermal effects will be a dominating source of attraction. We have determined temperature criteria that must be fulfilled for the fractional separation dependence to be observable. Thermal corrections will be important already at temperatures less than 1 K. We further make some comments on a recent measurement of the Casimir force.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-47653 (URN)10.1016/S0167-9317(99)00486-4 (DOI)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2022-03-16
2. Fractional van der Waals interaction between thin metallic films
Open this publication in new window or tab >>Fractional van der Waals interaction between thin metallic films
2000 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 61, no 3, p. 2204-2210Article in journal (Refereed) Published
Abstract [en]

The van der Waals (vdW) interaction between thin metallic films varies with separation as the separation to a fractional power. This is in contrast to the usual integer-power separation dependence between objects such as atoms, dielectric films, or thick metallic films. We have calculated the free energy of attraction between sheets of gold, silver, copper, beryllium, and tungsten numerically using experimentally found dielectric functions. The results are compared with the corresponding analytical results obtained using simple model dielectric functions. We have investigated how thin the metallic films must be in order for the fractional vdW interaction to be present. To our knowledge, fractional vdW interaction has not yet been confirmed experimentally.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-49827 (URN)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2022-03-16
3. Comment on "Calculation of the Casimir force between imperfectly conducting plates"
Open this publication in new window or tab >>Comment on "Calculation of the Casimir force between imperfectly conducting plates"
2000 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 61, no 4Article in journal, Editorial material (Other academic) Published
Abstract [en]

In a recent paper [Phys. Rev. A 59, R3149 (1999)] Lamoreaux reported calculations of the Casimir force. The experimentally found permittivity was used in the calculations. Large deviations were found between numerically evaluated forces and forces derived from a series expanded plasma model. We would like to comment on a few results presented in this work. First, we claim that important features of the imaginary component of the permittivity of copper, presented in Fig. 1(a) are due to the interpolation procedure and are not caused by physical phenomena. These features influence the calculated permittivity for imaginary frequencies, which is the quantity used to calculate the Casimir attraction. Second, we discuss the extrapolation procedure used for low frequencies. The results depend substantially on how this extrapolation is performed.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-49786 (URN)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2022-03-16
4. van der Waals energy of an atom in the proximity of thin metal films
Open this publication in new window or tab >>van der Waals energy of an atom in the proximity of thin metal films
2000 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 61, no 5, p. art. no.-052703Article in journal (Refereed) Published
Abstract [en]

The van der Waals energy of a ground-state atom (or molecule) placed between two metal films is calculated at finite temperature. The attraction between thin metal films and a polarizable object can have half-integer separation dependence. This is in contrast to the usual integer separation dependence, shown for instance in the attraction between an atom and a solid surface. We examine how film thickness, retardation, and temperature influence the interaction. To illustrate the effect of finite thickness of the metal film we calculated the van der Waals energy of ground-state hydrogen and helium atoms, and hydrogen molecules, between thin silver films. We finally, briefly, discuss the possibility to measure this effect.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-49751 (URN)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2022-03-16
5. Thermal effects on the Casimir force in the 0.1-5 mu m range
Open this publication in new window or tab >>Thermal effects on the Casimir force in the 0.1-5 mu m range
2000 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 84, no 20, p. 4757-4760Article in journal (Refereed) Published
Abstract [en]

The vacuum stresses between a metal half-space and a metal sphere were recently measured at room temperature, in the 0.6-6 mu m range, with an estimated accuracy of 5%. In the interpretation it was assumed that the accuracy was not good enough for observing any thermal effects. We claim that thermal effects are important in this separation range and back up this claim with numerical calculations of the Casimir force at zero temperature and at 300 K, based on tabulated optical data of gold, copper, and aluminum. The effects of dissipation and temperature are investigated and we demonstrate the importance of considering these two corrections together.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-49749 (URN)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2022-03-16
6. Retardation-enhanced van der Waals force between thin metal films
Open this publication in new window or tab >>Retardation-enhanced van der Waals force between thin metal films
2000 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 62, no 11, p. 7523-7526Article in journal (Refereed) Published
Abstract [en]

We recently investigated the van der Waals force between thin metal films. Under certain conditions this force decrease with separation to a fractional power. In the present work we use optical data of metals and the zero-temperature Lifshitz formalism to demonstrate a retardation effect. The retarded attraction between thin metal films may be larger than the nonretarded attraction. This property is related to a comparatively weak retardation dependence of the energy that originates from the transverse magnetic modes. At separations where the transverse electric modes give a significant contribution, the net effect can actually be an increased attraction. This effect vanishes with increasing film thickness and with increasing dissipation.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-47585 (URN)10.1103/PhysRevB.62.7523 (DOI)
Note
Original Publication: Mathias Boström and Bo Sernelius, Retardation-enhanced van der Waals force between thin metal films, 2000, Physical Review B Condensed Matter, (62), 11, 7523-7526. http://dx.doi.org/10.1103/PhysRevB.62.7523 Copyright: American Physical Society http://www.aps.org/Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2022-03-16

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