With the discovery of high-temperature superconductivity in cuprates, understanding pairing mechanisms in strongly correlated phases of matter has prevailed as one of the most challenging problems in contemporary condensed matter physics. In particular, detailed microscopic insights into the relevant physics can open the way towards a targeted design of novel materials with high critical temperatures at ambient conditions. Very recently, the Ruddlesen-Popper bilayer perovskite nickelate La₃Ni₃O₇ (LNO) has joined the family of bulk superconductors above the boiling point of liquid nitrogen, whereby extraordinarily high critical temperatures (T_c) of 80 K at applied pressures above 14 GPa have been reported [1]. It has been argued that the low-energy physics of LNO can be described by the single band, strongly correlated mixed dimensional bilayer t-J model [2,3]. Our investigation of this bilayer system, utilizing density matrix renormalization group techniques, establishes an intricate understanding of the model and the magnetically induced pairing through comparison to the perturbative limit of dominating inter-layer spin couplings. In particular, this allows us to explain appearing finite-size effects as well as the role of all coupling parameters in the Hamiltonian, and we make predictions for binding energies and spin gaps in the two-dimensional limit. We estimate critical temperatures of the Berezinskii-Kosterlitz-Thouless transition in the perturbative regime, and discuss possible implications for the fate of T_c of LNO.

[1] Sun et al., Nature 621 (2023)

[2] Qu et al., arXiv:2307.16873 (2023)

[3] Oh et al., arXiv:2307.15706 (2023)