Size effect for the Josephson plasma resonance in high-T_c superconductors

We formulate a theory for the size effect for the longitudinal Josephson plasma oscillations in a 1D intrinsic Josephson-junction array (IJJA) with a finite in-plane area. The charging energy of the superconducting layers causes the size-dependence of the plasma frequency. The size effect can be described as a quantum correction for the superconducting phase differences in this system. The plasma oscillations become unstable as the in-plane area decreases. It is predicted that the resonant state in which the single-particle plasma excitation resonates with thermally-excited plasma oscillations appears in an IJJA with a small in-plane area.