Odd-frequency pairing in the Kondo lattice

Abstract

We discuss the possibility that heavy-fermion superconductors involve odd-frequency triplet pairing. A key technical innovation here is a Majorana representation for the local moments which avoids the use of a Gutzwiller projection. We employ the Kondo lattice model and develop a mean-field theory for odd-frequency pairing that entails pairing between local moments and conduction electrons, as described by a spinor order parameter. We confirm that the Meissner stiffness is positive and the state is stable. A residual band of gapless quasiparticles whose spin and charge coherence factors vanish linearly in energy, decouples from the condensate. The unusual energy dependence of these coherence factors leads to a ${\mathit{T}}^{3}$ NMR relaxation rate at a conduction electron site that coexists with a linear specific heat. Two verifiable predictions of the theory are (i) that a Korringa relaxation will fail to develop in heavy-fermion superconductors, even in the limit of strong pair breaking and severe gaplessness and (ii) that the hitherto unmeasured NMR relaxation rate at the actinide or rare-earth site will become exponentially activated in the superconducting phase.