Two-stage superconductivity in the Hatsugai-Kohmoto-BCS model

Abstract

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

10 pages, 8 figures

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