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

Abstract

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-${T}_{c}$ cuprate superconductors (HTCS) and use it to estimate---from available infrared data---the change below ${T}_{c}$ of the c-axis kinetic energy, $〈{H}_{c}〉,$ in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ $(\ensuremath{\delta}\ensuremath{\approx}0.45,0.25,0.07),$ ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8},$ and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{10}.$ In all these compounds $〈{H}_{c}〉$ decreases below ${T}_{c}$ and except for ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ the change of $〈{H}_{c}〉$ 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 tunneling mechanism.