Collective modes in a tight-binding model of layered narrow-band anisotropic superconductors

The collective modes in layered narrow-tight-binding-band superconductors are investigated within the ladder-diagram approximation with the vacuum-polarization correction. The in-plane nearest-neighbor interaction and the interplane nearest-neighbor tunneling are assumed. For the extended s-wave and d-wave states, the in-plane and out-of-plane longitudinal plasma frequencies (plasmon energies) in the long-wavelength limit are calculated as functions of hole density and temperature T. Their expressions almost coincide with those for the normal-state electrons in the same tight-binding model. Both of the in-plane and out-of-plane results are almost unaffected by the anisotropy of the order parameter, and almost do not depend on T. The out-of-plane plasma frequency can be smaller than the superconducting energy gap for the extended s-wave state. The obtained in-plane and out-of-plane plasma frequencies (though they are for the longitudinal modes) are compared with the recent experimental results for the transverse plasma frequencies in high-${\mathit{T}}_{\mathit{c}}$ superconductors. © 1996 The American Physical Society.