Abstract
The Casimir effect between type-II superconducting plates in the coexisting phase of a superconducting phase and a normal phase is investigated. The dependence of the optical conductivity of the superconducting plates on the external magnetic field is described in terms of the penetration depth of the incident electromagnetic field, and the permittivity along the imaginary axis is represented by a linear combination of the permittivities for the plasma model and Drude models. The characteristic frequency in each model is determined using the force parameters for the motion of the magnetic field vortices. The Casimir force between parallel YBCO plates in the mixed state is calculated, and the dependence on the applied magnetic field and temperature is considered.
Highlights
The Casimir effect [1], which means that perfectly conductive plates attract each other due to the quantum fluctuations of the electromagnetic field in a vacuum, is an interesting macroscopic quantum effect
Based on Casimir’s prediction, Lifshitz presented the generalized theory of the Casimir effect, which can be applied to dielectric bodies, including metals, and Lamoreaux [2] verified the Lifshitz theory via precise measurement of the Casimir force between metallics plates
The dependence of the Casimir force between superconductive plates on the magnetic field can be calculated if the penetration depth can be expressed as a function of the external magnetic field
Summary
The Casimir effect [1], which means that perfectly conductive plates attract each other due to the quantum fluctuations of the electromagnetic field in a vacuum, is an interesting macroscopic quantum effect. The dependence of the Casimir force between superconductive plates on the magnetic field can be calculated if the penetration depth can be expressed as a function of the external magnetic field. The Casimir effect between type-II superconductors under the external magnetic field cannot be understood without considering the interactions between the magnetic flux and the quantum fluctuation of the vacuum. We focused on the dependence of the Casimir force between high-Tc superconductors in the mixed state on the applied magnetic field. The optical properties required to calculate the Casimir force using the Lifshitz theory are the permittivities at arbitrary Matsubara frequencies along the imaginary axis. According to the theory by Villarreal and Caballero-Benitez for the Casimir force between YBCO plates in the superconductive state without magnetic field, the dielectric function is expressed as follows: s(ω, T) =. YBCO has anisotropy for the dielectric permittivity even in the absence of a magnetic field, we consider only the anisotropy arising from vortices
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