Approximate tight-binding sum rule for the superconductivity related change of c-axis kinetic energy in multilayer cuprate superconductors

We present an extension of the c-axis tight-binding sum rule discussed by Chakravarty, Kee, and Abrahams [Phys. Rev. Lett. 82, 2366 (1999)] that applies to multilayer high-Tc cuprate superconductors (HTCS) and use it to estimate--from available infrared data--the change below Tc of the c-axis kinetic energy, Hc, in YBa2Cu3O(7-delta) (delta=0.45,0.25,0.07), Bi2Sr2CaCu2O8, and Bi2Sr2Ca2Cu3O10. In all these compounds Hc decreases below Tc and except for Bi2Sr2CaCu2O8 the change of Hc is of the same order of magnitude as the condensation energy. This observation supports the hypothesis that in multilayer HTCS superconductivity is considerably amplified by the interlayer tunnelling mechanism.