Orbital-Selective $d$-wave Superconductivity in the Two-Band $t$-$J$ Model: Possible Applications to La$_3$Ni$_2$O$_7$

TL;DR

This study uses variational Monte Carlo to show that in a two-band $t$-$J$ model, superconductivity is orbital-selective and primarily emerges from the itinerant orbital, with implications for nickelate superconductors.

Contribution

It reveals the orbital-selective nature of $d$-wave superconductivity in a two-band model, emphasizing the role of multi-orbital physics beyond single-band frameworks.

Findings

Superconductivity is robust and orbital-selective, originating mainly from the itinerant orbital.

Increasing occupancy of the localized orbital suppresses superconductivity.

Suppressing localized orbital involvement could enhance the critical temperature $T_c$.

Abstract

We investigate superconductivity in a two-band $t$-$J$ model consisting of an itinerant orbital (orbital-0) and a quasi-localized orbital (orbital-1) using variational Monte Carlo. A robust orbital-selective $d$-wave superconducting state is found to emerge exclusively from the itinerant orbital. An analysis of the superexchange energy hierarchy shows that the quasi-localized orbital-1 competes with superconductivity by favoring local inter-orbital bound states, which act as energy defects and disrupt phase coherence. Consistently, the superconducting order parameter is monotonically suppressed as the occupancy of orbital-1 increases. Motivated by superconductivity in nickelate La$_3$Ni$_2$O$_7$, these results highlight the essential role of multi-orbital physics beyond the single-band $t$-$J$ framework and point to a concrete route to enhance $T_c$: suppressing the involvement of localized $d_{z^2}$-derived orbitals.