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This paper studies how having two electronic orbitals per atom changes superconductivity in a simple model. The authors find that a robust d-wave superconducting state appears only in the more mobile orbital (called orbital-0, similar to a dx2−y2 orbital). A second, more localized orbital (orbital-1, dz2-like) does not pair and instead forms local bound states with orbital-0 electrons that act like defects and weaken superconductivity.
The team wrote down a two-band version of the t–J model, a standard simplified model for strongly interacting electrons. In their setup orbital-0 has large hopping (moves easily) while orbital-1 hops much less. They studied this model at one electron per site (quarter filling) using a numerical variational Monte Carlo (VMC) method. The VMC used Gutzwiller-projected trial wavefunctions, which enforce that sites are not doubly occupied. Some concrete numbers used in the study are t11 ≈ 0.2 t00 and t01 ≈ 0.5 t00 as realistic for nickelate materials, with t00 set as the unit and U (the on-site repulsion) taken as 8. Some simulations used a 20×20 lattice and a doping level of δ = 0.16.
At a physical level the result comes from the pattern of virtual hopping processes called superexchange. The most mobile orbital-0 gains the largest antiferromagnetic superexchange energy and thus supports the spin correlations that favor d-wave pairing. But the presence of orbital-1 allows a strong inter-orbital, spin-independent attraction that binds an orbital-1 electron to an orbital-0 electron on a neighbor. Those bound pairs do not participate in the coherent spin correlations needed for a superconducting condensate. Numerically, the authors report a clear orbital-selective pairing amplitude: the pairing on orbital-0 is robust, while pairing amplitudes on orbital-1 and between orbitals are vanishingly small. The superconducting order parameter is steadily reduced as the occupancy of orbital-1 grows.
Why this matters: the result highlights that multi-orbital effects can change or even suppress superconductivity predicted by single-orbital models. The authors point to recent high-temperature superconductivity reported in the bilayer nickelate La3Ni2O7 as a motivating example. Their calculations suggest a concrete route to raise the superconducting critical temperature Tc in such materials: reduce the involvement of the localized dz2-derived orbital so fewer electrons occupy orbital-1 and fewer energy-defect bound states form.
Important caveats and uncertainties: this work studies a simplified two-band t–J model and omits some effects such as Hund’s coupling. The analysis focuses on quarter filling and on d-wave pairing channels; the authors note a full exploration of the phase diagram was not done. The numerical method uses variational trial states (Gutzwiller-projected mean-field states), so conclusions depend on the chosen ansatz. The authors also place their work in the context that even for the single-band t–J model the stability of long-range superconducting order remains debated. Thus the paper presents a clear theoretical mechanism and prediction, but applying it directly to real materials will require further modeling and experimental tests.