The paper shows that a non-Hermitian boundary effect can increase short-range pairing tendencies in a model of interacting electrons on a moiré triangular lattice. When hopping is made non-reciprocal so that electrons prefer one direction, eigenstates pile up at an open boundary — the non-Hermitian skin effect (NHSE). In an intermediate range of non-reciprocity (a “golden window” of the parameter γ roughly between 0.5 and 1.2 times the ordinary hopping t, with a peak near γ≈1.0t) this boundary pileup raises local double occupancy by up to about 21% for a representative interaction strength U=4t. The authors stress that they do not claim this proves long-range superconducting order; instead they report enhanced finite-cluster pairing correlations.

To reach these conclusions the authors studied a non-Hermitian Hubbard model on triangular moiré lattices at half filling. Non-reciprocity is introduced by asymmetric hopping along one direction (right hopping t+γ versus left hopping t−γ). They scanned interaction strength U and non-reciprocity γ using exact diagonalization on small clusters (mainly a 3×3 triangular cluster) and also checked results with a non-Hermitian variant of density matrix renormalization group (NH-DMRG). Their main observables were the double occupancy D (the fraction of sites with two electrons), a skin order parameter that measures asymmetric particle accumulation at the boundary, and a pairing susceptibility χ_SC that sums equal-time pair correlations.

The physical picture is simple at a qualitative level. The NHSE pushes many single-particle states toward the boundary. That increases the local density of states (LDOS) at the edge and so raises the local tendency for two electrons to occupy the same site. This LDOS amplification competes with over-localization: at small to moderate γ the boundary amplification strengthens local pairing, but at larger γ wavefunctions become too localized and the pairing response falls. The authors give an approximate skin-penetration length λ_skin≈1/ln[(t+γ)/(t−γ)] and estimate how boundary LDOS can be exponentially amplified, which sets the scale of the dome-shaped response in γ.