Analytical results on Casimir forces for conductors with edges and tips
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 s...
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| Format: | Article |
| Language: | en_US |
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National Academy of Sciences
2011
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| Online Access: | http://hdl.handle.net/1721.1/66993 https://orcid.org/0000-0002-0262-3645 https://orcid.org/0000-0002-1112-5912 |
| _version_ | 1811076813628112896 |
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| author | Emig, Thorsten Graham, Noah Faghfoor Maghrebi, Mohammad Rahi, Sahand Jamal Jaffe, Robert L. Kardar, Mehran |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Emig, Thorsten Graham, Noah Faghfoor Maghrebi, Mohammad Rahi, Sahand Jamal Jaffe, Robert L. Kardar, Mehran |
| author_sort | Emig, Thorsten |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T10:27:59Z |
| format | Article |
| id | mit-1721.1/66993 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:27:59Z |
| publishDate | 2011 |
| publisher | National Academy of Sciences |
| record_format | dspace |
| spelling | mit-1721.1/669932022-09-30T21:20:31Z Analytical results on Casimir forces for conductors with edges and tips Emig, Thorsten Graham, Noah Faghfoor Maghrebi, Mohammad Rahi, Sahand Jamal Jaffe, Robert L. Kardar, Mehran Massachusetts Institute of Technology. Department of Physics Kardar, Mehran Faghfoor Maghrebi, Mohammad Rahi, Sahand Jamal Jaffe, Robert L. Kardar, Mehran 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. National Science Foundation (U.S.) (grant PHY08-55426) National Science Foundation (U.S.) (grant DMR-08-03315) United States. Defense Advanced Research Projects Agency (Contract S-000354) Deutsche Forschungsgemeinschaft (DFG) (Grant EM70/3) United States. Dept. of Energy (cooperative research agreement DE-FG02-05ER41360) 2011-11-09T22:47:27Z 2011-11-09T22:47:27Z 2011-04 2010-12 Article http://purl.org/eprint/type/JournalArticle 0027-8424 1091-6490 http://hdl.handle.net/1721.1/66993 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 https://orcid.org/0000-0002-0262-3645 https://orcid.org/0000-0002-1112-5912 en_US http://dx.doi.org/10.1073/pnas.1018079108 Proceedings of the National Academy of Sciences of the United States of America 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. application/pdf National Academy of Sciences PNAS |
| spellingShingle | Emig, Thorsten Graham, Noah Faghfoor Maghrebi, Mohammad Rahi, Sahand Jamal Jaffe, Robert L. Kardar, Mehran Analytical results on Casimir forces for conductors with edges and tips |
| title | Analytical results on Casimir forces for conductors with edges and tips |
| title_full | Analytical results on Casimir forces for conductors with edges and tips |
| title_fullStr | Analytical results on Casimir forces for conductors with edges and tips |
| title_full_unstemmed | Analytical results on Casimir forces for conductors with edges and tips |
| title_short | Analytical results on Casimir forces for conductors with edges and tips |
| title_sort | analytical results on casimir forces for conductors with edges and tips |
| url | http://hdl.handle.net/1721.1/66993 https://orcid.org/0000-0002-0262-3645 https://orcid.org/0000-0002-1112-5912 |
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