Inhomogeneous superconductor in an ac field: Application to the pseudogap region

The behavior of an inhomogeneous superconductor in an external ac field is studied. General equations describing the ac response are formulated. Special attention is paid to the case of a layered conductor containing superconducting “islands.” A system of this type displays “pseudogap” properties. The surface impedance Z is evaluated. It is shown that $\mathrm{Re}Z\ne |\mathrm{Im}Z|$ and that their difference is $\Delta Z\propto {\omega }^{-1/2},$ where ω is the frequency of the ac field.