Casimir Effect between Superconducting Plates in the Mixed State

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.