Abstract
The effective microwave surface impedance for a layered structure made of a thin type-II superconducting film as well as a dielectric substrate is theoretically investigated. We consider the superconducting film with thickness comparable or smaller than the penetration depth in the parallel magnetic field, in which a vortex chain is present in the central plane of film. The total effective microwave surface impedance is shown to consist of two parts, one represents the Meissner state response which can be calculated by the usual impedance transform technique, and the other not obtainable from the impedance transform is the vortex response. The effective surface resistance and reactance due to the vortex chain are specifically numerically investigated as functions of the thicknesses of film and dielectric, static magnetic field and microwave frequency as well. For the frequency-dependent surface impedance, numerical results reveal that there exists a crossover frequency such that the surface resistance is equal to the surface reactance. This crossover frequency is further proven to be equal to the depinning frequency for a vortex system.
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