Superconducting-state enhancement of thermal conductivity in the cuprates: Correlation with the pair density

The systematics of the superconducting-state enhancements of in-plane thermal conductivity for $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ (Y-123), ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$Ca${\mathrm{Cu}}_2$ ${\mathrm{O}}_8$, ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$Cu${\mathrm{O}}_6$, and ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ single crystals are examined. For Y-123 the enhancements are shown to correlate with specific-heat jumps, a measure of the superconducting pair density. The substantially larger enhancements observed for Y-123 are attributed to the condensate arising from oxygen-filled CuO chains. We discuss the constraints imposed by measurements of microwave conductivity on the electronic contribution to this phenomenon.