  A residual linear term is observed in the thermal conductivity of
optimally-doped Bi-2212 at very low temperatures whose magnitude is in
excellent agreement with the value expected from Fermi-liquid theory and the
d-wave energy spectrum measured by photoemission spectroscopy, with no
adjustable parameters. This solid basis allows us to make a quantitative
analysis of thermodynamic properties at low temperature and establish that
thermally-excited quasiparticles are a significant, perhaps even the dominant
mechanism in suppressing the superfluid density in cuprate superconductors
Bi-2212 and YBCO.
