Some exotic phenomena related to vortices in high-T_c and heavy fermion superconductors

Discussions are given on two topics. The superconducting current along the c-axis of a cuprate superconductor flows through the Josephson coupling between the CuO₂ layers. The superconducting current is coupled with the electromagnetic field, generating a Josephson plasma with a low frequency. The Josephson plasma strongly interacts with the vortices, and thus the plasma frequency is strongly dependent on magnetic field and temperature. Since the interaction is strong enough, the plasma will be excited by the vortex flow. The other topic concerns a new state appearing in a high magnetic field near H_c2 of heavy fermion and intermediate valence superconductors, such as UPd₂Al₃ and CeRu₂. It is predicted that the order parameter in the state is spatially modulated, and planar nodes of the order parameter are periodically aligned perpendicular to the vortices. The nature of the state will be discussed in relation to anomalous properties of the magnetization, the crystal dilation, and other physical quantities observed in the vortex state of the compounds.