A Simple Solvable Model for Heavy Fermion Superconductivity from the Two-Fluid Normal State

We propose an exactly solvable momentum-space Kondo-BCS model to study heavy fermion superconductivity. The Kondo interaction is local in momentum space, which can be derived from an Anderson lattice with a Hatsugai-Kohmoto interaction between $f$-electrons. By increasing the Kondo interaction, the model exhibits a crossover from a weak-coupling BCS superconductor to a strong-coupling heavy fermion superconductor featured with a large gap ratio and a large specific heat jump anomaly. Accordingly, the normal state evolves from a Fermi liquid above the BCS superconductor to a non-Fermi liquid two-fluid state above the heavy fermion superconductor. The two-fluid normal state also leads to two types of Cooper pairs, one between conduction electrons, the other between composite fermions formed by conduction electrons and $f$-spins, which is responsible for the strong coupling behaviors of heavy fermion superconductivity.