Collective charge density fluctuations in superconducting layered systems with bilayer unit cells

Collective modes of bilayered superconducting superlattices (e.g., YBCO) are investigated within the conserving gauge-invariant ladder diagram approximation including both the nearest interlayer single electron tunneling and the Josephson-type Cooper pair tunneling. By calculating the density-density response function including Coulomb and pairing interactions, the authors examine the two collective mode branches corresponding to the in-phase and out-of-phase charge fluctuations between the two layers in the unit cell. The out-of-phase collective mode develops a long wavelength plasmon gap whose magnitude depends on the tunneling strength with the mode dispersions being insensitive to the specific tunneling mechanism (i.e., single electron or Josephson). They also show that in the presence of tunneling the oscillator strength of the out-of-phase mode overwhelms that of the in-phase-mode at kparallel = 0 and finite kz, where kz and kparallel are respectively the mode wave vectors perpendicular and along the layer. They discuss the possible experimental observability of the phase fluctuation modes in the context of their theoretical results for the mode dispersion and spectral weight