AC response of Abrikosov vortices in layered superconductors

The linear AC response of the flux lines created by external magnetic fields perpendicular to the layers of the layered superconductor is calculated. We elaborate on the concept that flux lines in a layered superconductor are formed by two-dimensional (2D) vortices related to the Berezinskii-Kosterlitz-Thouless transition in high-Tc superconductors. Thermal fluctuations in the shifts of 2D-vortices forming flux lines are taken into account by means of Fokker-Planck equations for the 2D-vortex coordinates using the self-consistent potential including pinning. We concentrate on the case of small magnetic fields. The complex frequency dependent penetration length, the distribution of current density, and the frequency dependence of the surface impedance are calculated for samples of finite thickness. (orig.)