  The thermal conductivity kappa of the heavy-fermion metal CeCoIn5 was
measured in the normal and superconducting states as a function of temperature
T and magnetic field H, for a current and field parallel to the [100]
direction. Inside the superconducting state, when the field is lower than the
upper critical field Hc2, kappa/T is found to increase as T approaches absolute
zero, just as in a metal and in contrast to the behavior of all known
superconductors. This is due to unpaired electrons on part of the Fermi
surface, which dominate the transport above a certain field. The evolution of
kappa/T with field reveals that the electron-electron scattering (or transport
mass m^*) of those unpaired electrons diverges as H approaches Hc2 from below,
in the same way that it does in the normal state as H approaches Hc2 from
above. This shows that the unpaired electrons sense the proximity of the
field-tuned quantum critical point of CeCoIn5 at H^* = Hc2 even from inside the
superconducting state. The fact that the quantum critical scattering of the
unpaired electrons is much weaker than the average scattering of all electrons
in the normal state reveals a k-space correlation between the strength of
pairing and the strength of scattering, pointing to a common mechanism,
presumably antiferromagnetic fluctuations.
