Variation Monte Carlo Study on the bilayer t-J∥-J⊥ model for La₃Ni₂O₇

The discovery of high-temperature superconductivity (HTSC) in La₃Ni₂O₇ has aroused significant interest in exploring the pairing mechanism. Previous studies have proposed an effective dx²-y²-orbital bilayer t-J∥-J⊥ model, in which the electrons of the dx²-y² orbital are charge carriers, which are subject to the intralayer antiferromagnetic (AFM) superexchange J∥ and the large interlayer AFM superexchange J⊥≈ 2J∥, with the latter transferred from the nearly half-filled and hence localized dz² orbital through the strong Hund's rule coupling. Here we study this model by the variational Monte Carlo (VMC) simulation and find a dominant interlayer s-wave pairing, in which the SC order parameters have a drastic improvement compared with those of the mean field (MF) type of theories. In real materials, the Hund's coupling is finite, leading to reduced J⊥, dictating that the MF-type theories have difficulty explaining the HTSC. However, our VMC calculations find that even for effective J⊥ as weak as J⊥=J∥, the interlayer pairing is still considerably large and can be compared with the Tc observed in experiments, which is very weak in MF-type theories. This result indicates the important role of the Gutzwiller projection in improving the Tc, which is ignored in the MF-type theories. In addition, our results show that suppressed interlayer hopping can promote interlayer pairing, which is consistent with the fact that the interlayer hopping of the dx²-y² orbital in La₃Ni₂O₇ is very weak. Our research offers a new perspective for understanding the pairing mechanism of bilayer nickelates and provides a reference for recent ultra-cold atom experiments in mixed-dimensional systems.