Correlation between the Josephson coupling energy and the condensation energy in bilayer cuprate superconductors

Abstract

We review some previous studies concerning the intrabilayer Josephson plasmons and present ellipsometric data of the c-axis infrared response of almost optimally doped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}.$ The c-axis conductivity of this compound exhibits the same kind of anomalies as that of underdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$ We analyze these anomalies in detail and show that they can be explained within a model involving the intrabilayer Josephson effect and variations of the electric field inside the unit cell. The Josephson coupling energies of different bilayer compounds obtained from the optical data are compared with the condensation energies and it is shown that there is a reasonable agreement between the values of the two quantities. We argue that the Josephson coupling energy, as determined by the frequency of the intrabilayer Josephson plasmon, represents a reasonable estimate of the change of the effective c-axis kinetic energy upon entering the superconducting state. It is further explained that this is not the case for the estimate based on the use of the simplest ``tight-binding'' sum rule. We discuss possible interpretations of the remarkable agreement between the Josephson coupling energies and the condensation energies. The most plausible interpretation is that the interlayer tunneling of the Cooper pairs provides the dominant contribution to the condensation energy of the bilayer compounds; in other words that the condensation energy of these compounds can be accounted for by the interlayer tunneling theory. We suggest an extension of this theory, which may also explain the high values of ${T}_{c}$ in the single-layer compounds ${\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}{\mathrm{CuO}}_{6}$ and ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4},$ and we make several experimentally verifiable predictions.