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

• Published in: New journal of physics 2022-10, Vol.24 (10), p.103019
• Main Authors: Li, Yu, Mishra, Vivek, Zhou, Yi, Zhang, Fu-Chun
• Format: Article
• Language: English
• Subjects: Cuprates; Electrons; Entropy; Fermi liquids; Fermi surfaces; Ginzburg–Landau theory; Green's functions; non-Fermi liquid; Order parameters; Phase transitions; Physics; strongly-correlated system; Superconductivity; Unconventional superconductivity
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ac9548

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–Kohomoto (HK) model has suggested a non-Fermi liquid ground state whose Green’s function resembles the Yang–Rice–Zhang ansatz for cuprates (2020 Phillips et al Nat. Phys. 16 1175). 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-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 c that is followed by a sudden increase of the superconducting order parameter at a lower temperature T c ′ < T c . At the first stage, T c ′ < T < T 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 c ′ , 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.