Casimir force between sharp-shaped conductors

Mohammad F. Maghrebi 1, Sahand Jamal Rahi 1, 2, Thorsten Emig 3, Noah Graham 4, Robert L. Jaffe 1, Mehran Kardar 1

Proceeding of the national academy of sciences 108 (2011) 6867-6871

Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery 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 to wedges and cones. The 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 MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest.

  • 1. Department of Physics,
    Massachusetts Institute of Technology
  • 2. Center for Studies in Physics and Biology,
    The Rockefeller University
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 4. Middlebury College,
    Middlebury Colleg