Simple solvable model for heavy-fermion superconductivity from the two-fluid normal state

Heavy-fermion superconductors exhibit unusual properties such as low transition temperatures, large specific heat jumps, and normal states with universal two-fluid behaviors. Standard theoretical models such as the Anderson or Kondo lattices often require uncontrolled approximations to solve. Here, we propose an exactly solvable Kondo lattice model with a local-in-momentum Kondo interaction, which can be derived from an Anderson lattice with a Hatsugai-Kohmoto interaction between $f$ electrons. As the Kondo coupling increases, the normal state evolves from a Fermi liquid to a non-Fermi liquid two-fluid state. With a pairing interaction between electrons, the model exhibits a crossover from a weak-coupling superconductor to a strong-coupling one showing many important features of heavy-fermion superconductivity, including the formation of Kondo-induced composite-fermion Cooper pairs, the analog of heavy-electron Cooper pairs in real materials.