Analytical results on Casimir forces for conductors with edges and tips
Name
Kardar-2011-April-Analytical results on Casimir.pdf
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Author(s)
Emig, Thorsten
Graham, Noah
Faghfoor Maghrebi, Mohammad
Rahi, Sahand Jamal
Jaffe, Robert L.
Kardar, Mehran
Date Issued
April 2011
Journal
Proceedings of the National Academy of Sciences of the United States of America
Publisher
National Academy of Sciences
Citation
Maghrebi, M. F. et al. “Analytical results on Casimir forces for conductors with edges and tips.” Proceedings of the National Academy of Sciences 108 (2011): 6867-6871. Web. 9 Nov. 2011. © 2011 National Academy of Sciences
Version
Final published version
Abstract
Casimir forces between conductors at the submicron scale are paramount to the design and operation of microelectromechanical devices. However, these forces depend nontrivially on geometry, and existing analytical formulae and approximations cannot deal with realistic micromachinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically wedges and cones. The Casimir interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of microelectromechanical devices. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe. We find an unexpectedly large temperature dependence of the force in the cone tip which is of immediate relevance to experiments.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1073/pnas.1018079108
