Two-stage superconductivity in the Hatsugai–Kohomoto-BCS model

Superconductivity in strongly correlated electrons can emerge out from a normal state that is beyond the Landau's Fermi liquid paradigm, often dubbed as "non-Fermi liquid". While theory for non-Fermi still not yet conclusive, recent study on exactly-solvable Hatsugai-Kohmoto (HK) model has suggested ground whose Green's function resembles Yang-Rice-Zhang ansatz cuprates [P. W. Phillips, L. Yeo and E. Huang, Nat. Phys. $\bf{16}$, 1175 (2020)]. Similar to effect of on-site Coulomb repulsion Hubbard model, repulsive interaction HK divides momentum space into three parts: empty, single-occupied double-occupied regions, are separated each other by two distinct surfaces. In presence an additional Bardeen-Cooper-Schrieffer (BCS)-type pairing moderate strength, we show system exhibits "two-stage superconductivity" feature temperature decreases: first-order superconducting transition occurs at $T_{\rm c}$ followed sudden increase order parameter lower c}^{\prime}<T_{\rm c}$. At first stage, c}^{\prime}<T<T_{\rm c}$, arises entropy released only vicinity surfaces; while second $T<T_{\rm c}^{\prime}$, becomes significant further deep (single-occupied) region sea. The phase transitions analyzed within Ginzburg-Landau theory. Our work sheds new light unconventional superconductivity electrons.