Using a two-channel Anderson model, we develop a theory of composite pairing in the 115 family of heavy fermion superconductors that incorporates the effects of $f$-electron valence fluctuations. Our calculations introduce “symplectic Hubbard operators”: an extension of the slave boson Hubbard operators that preserves both spin rotation and time-reversal symmetry in a large $N$ expansion, permitting a unified treatment of anisotropic singlet pairing and valence fluctuations. We find that the development of composite pairing in the presence of valence fluctuations manifests itself as a phase-coherent mixing of the empty and doubly occupied configurations of the mixed valent ion. This effect redistributes the $f$-electron charge within the unit cell. Our theory predicts a sharp superconducting shift in the nuclear quadrupole resonance frequency associated with this redistribution. We calculate the magnitude and sign of the predicted shift expected in CeCoIn${}_5$.

• Received 4 April 2011

DOI:https://doi.org/10.1103/PhysRevB.84.064514