Josephson coupling energy and c-axis sum rules in Bi2Sr2Ca2Cu3O10

Polarized reflectivity measurements were performed on a textured Bi2Sr2Ca2Cu3O10 polycrystal. The far infrared c-axis optical conductivity exhibits similarities with other multilayer superconductors. Namely, a broad band develops around 450 cm−1 and nearby phonon anomalies are observed as temperature is decreased. In agreement with lattice dynamics calculation, two oxygen bond-bending modes are found at 362 cm−1 and 392 cm−1. In contrast with bilayer compounds, this latter phonon mode grows in intensity as temperature decreases. In order to describe quantitatively the appearance of the 450 cm−1 peak in the superconducting state, we used the Josephson superlattice model to fit experiments. In this model, the multilayer superconductor is considered as a stack of superconducting layers with non-equivalent intralayer and interlayer Josephson coupling constants. The temperature dependence of the interlayer Josephson coupling energy is extracted from the fit and compared to a possible change in c-axis kinetic energy deduced from an approximate tight-binding sum rule.