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Motivated by the recent discovery of superconductivity in square-planarnickelates as well as by longstanding puzzling experiments in heavy-fermionsuperconductors, we study Cooper pairing between correlated $d$-electronscoupled to a band of weakly-correlated electrons. We perform self-consistentlarge N calculations on an effective $t-J$ model for the $d$-electrons withadditional hybridization. Unlike previous studies of mixed-valent systems, wefocus on parameter regimes where both hybridized bands are relevant todetermining the pairing symmetry. For sufficiently strong hybridization, wefind a robust $s+id$ pairing which breaks time-reversal and point-groupsymmetries in the mixed-valent regime. Our results illustrate how intrinsicallymulti-band systems such as heavy-fermions can support a number of highlynon-trivial pairing states. They also provide a putative microscopicrealization of previous phenomenological proposals of $s+id$ pairing andsuggest a potential resolution to puzzling experiments in heavy-fermionsuperconductors such as U$_{1-x}$Th$_x$Be$_{13}$ which exhibit twosuperconducting phase transitions and a full gap at lower temperatures.

Theory of $(s+id)$ pairing in mixed-valent correlated metals