Time-dependent equations for phase differences and a collective mode in Josephson-coupled layered superconductors

A time-dependent equation for the interlayer phase differences is derived for Josephson-coupled layered superconductors. It generalizes the sine-Gordon equation for the phase in a standard Josephson junction to the case of multilayer systems. With the help of this equation, the dispersion of a collective mode is found at low temperatures. In highly anisotropic systems the gap in the spectrum of this mode lies below the superconducting gap and is suppressed strongly by a magnetic field parallel to the layers. The effect of this mode on the dielectric function and specific heat is calculated.