Abstract
We present a theory of the interplane conductivity of bilayer high temperature superconductors, focusing on the effect of quantal and thermal fluctuations on the oscillator strengths of the superfluid stiffness and the bilayer plasmon. We find that the opening of the superconducting gap and establishment of superconducting phase coherence each lead to redistribution of spectral weight over wide energy scales. The factor-of-two relation between the superfluid stiffness and the change below $T_c$ in the oscillator strength of the absorptive part of the conductivity previously derived for single-layer systems, is found to be substantially modified in bilayer systems.
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