Gapless fermi surfaces in superconducting CeCoIn5

According to Tanatar [Phys. Rev. Lett. 95, 067002 (2005)], the low-temperature thermal conductivity in Ce1-xLaxCoIn5, a multiband d-wave superconductor, reveals unexpected dependence on the concentration of defects as if one or more Fermi surface sheets remained ungapped below superconducting transition. The interior gap superfluidity mechanism, or unbalanced pairing, recently proposed by Liu and Wilczek [Phys. Rev. Lett. 90, 047002 (2003)] has been invoked as a possible origin of gaplessness. We indicate that the Fermi surface anisotropy in the real CeCoIn5 makes this explanation highly implausible. We emphasize the fundamental difference between unbalanced pairing of different Fermi entities and the formation of superconducting gaps on Fermi surfaces belonging to different bands. We also argue that interband interactions between electrons always induce a finite order parameter on all Fermi surfaces below the temperature of a superconducting transition. We calculate specific heat and thermal conductivity in a two-band model for a d-wave superconductor in the presence of defects. In our simple model, superconductivity originates on one Fermi surface, inducing a smaller gap on the other one. Impurities diminish the induced gap and increase the density of states, restoring rapidly the Wiedemann-Franz law for this Fermi surface. Our calculations are in agreement with experiment.