Analytical results on Casimir forces for conductors with edges and tips

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 108; no. 17; pp. 6867 - 6871
• Main Authors: Maghrebi, Mohammad F, Rahi, Sahand Jamal, Emig, Thorsten, Graham, Noah, Jaffe, Robert L, Kardar, Mehran
• Format: Journal Article
• Language: English
• Published: Washington National Academy of Sciences 26.04.2011; National Acad Sciences
• Subjects: Approximation; Conductivity; Cones; Coordinate systems; Cylinders; Dielectric materials; electrical equipment; electromagnetic field; Electromagnetism; equipment design; Geometric planes; Geometric shapes; Geometry; Metals; Parallel plates; Physical Sciences; quantum mechanics; Room temperature; Scalars; Temperature
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1018079108

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.