Drastic change of the Casimir force at the metal-insulator transition

Abstract

The dependence of the Casimir force on material properties is important for both future applications and to gain further insight on its fundamental aspects. Here we apply the general Lifshitz theory of the Casimir force to low-conducting compounds, or poor metals. For distances in the micrometer range, the Casimir force for a large variety of such materials is described by universal equations containing a few parameters: the effective plasma frequency p , dissipation rate ␥ of the free carriers, and electric permittivity ϱ for Ն p ͑in the infrared range͒. This theory of the Casimir force for poor metals can also describe inhomogeneous composite materials containing small regions with different conductivity. The Casimir force for systems involving samples made with compounds that have a metal-insulator transition shows a drastic change of the Casimir force within the transition region, where the metallic and dielectric phases coexist. Indeed, the Casimir force can increase by a factor of 2 near this transition.

Temperature dependence of the Casimir force for bulk lossy media

“…[8,9,10,11,12,13,14]). The zero-temperature contribution to the force, originating from quantum fluctuations of the electromagnetic field, is well understood.…”

Electromagnetic Eigenmodes in Matter. Van Der Waals-London and Casimir Forces

“…As it is well-known, the fluctuations theory [32] predicts Casimir forces between any pair of bodies, in contrast with our results, which give a vanishing force for two distinct dielectrics, for instance. The difference originates in the circumstance, usually overlooked, that the equivalent of our dispersion Equations (28) and (33) in the fluctuations theory have no solutions in some cases, as, for instance, for distinct dielectrics. The usual theorem of meromorphic functions, applied within the framework of the fluctuations theory [4][5][6], gives then a finite result, but it does not represent the energy of the eigenmodes.…”

“…If r 1,2 are the amplitudes of these fields (for a given polarization), then the dispersion Equations (28) and (33) are obtained from r 1 = r 2 e 2iκd . We note that |r 1,2 | 2 are the reflection coefficients, and for two perfectly reflecting bodies |r 1 | = |r 2 | = 1.…”

“…We can take the limit d → ∞ in Equation (33). It can be shown that this limit amounts formally to put e 2iκd = 0 [23].…”

“…It was shown recently [33] that the van der Waals-London or Casimir forces may change drastically in complex materials, like poor conductors for instance, both in their numerical coefficients and in their d-dependence. Some of such changes seem to be related to the high-frequency dielectric functions ε (ω → ∞), which is not unity anymore, in contrast with our Equation (3).…”