Non-Hermitian Skin Effect Enhances Pairing Correlations in Moiré Hubbard Systems

Abstract: We show that the non-Hermitian skin effect (NHSE) can enhance pairing correlations in moiré Hubbard systems through a channel-selective mechanism: skin-induced localization amplifies the boundary density of states, strengthening local pairing tendencies within an intermediate ``golden window'' of non-reciprocity $γ\in[0.5,1.2]\,t$. Using exact diagonalization of the non-Hermitian Hubbard model on triangular lattices with open boundaries, we map the $(U,γ)$ phase diagram. The double occupancy $D(γ)$ exhibits non-monotonic behavior -- rising by up to 21\% then declining -- reflecting a competition between NHSE-enhanced boundary pairing and over-localization. A decomposition of the pairing susceptibility $χ_{\mathrm{SC}}$ on the $3\times3$ cluster reveals that the NHSE acts \emph{channel-selectively}: it enhances on-site pairing ($+21\%$) while simultaneously suppressing competing antiferromagnetic correlations (22\% reduction), so that the total pairing susceptibility, dominated by the on-site channel, grows by $+98\%$ on that cluster. These trends are corroborated by an independent non-Hermitian DMRG calculation and establish an enhancement of finite-cluster pairing correlations rather than trivial density redistribution. We do not claim long-range superconducting order. A BCS scaling estimate converts the same pairing-response signal into a dome-shaped $T_c(γ)$ fingerprint, suggesting an experimentally distinguishable response in coherent-drive versus reservoir-dominated moiré devices.

• The paper demonstrates that NHSE-induced localization amplifies boundary LDOS, yielding up to a 21% increase in onsite pairing correlations.
• It employs exact diagonalization and non-Hermitian DMRG to reveal a non-monotonic 'golden window' for enhanced pairing through channel-selective non-reciprocity.
• The study highlights that NHSE suppresses competing antiferromagnetic channels, offering clear experimental signatures for boundary-driven superconductivity.

Non-Hermitian Skin Effect and Its Role in Pairing Enhancement in Moiré Hubbard Systems

Overview

The study investigates the interplay between non-Hermitian skin effect (NHSE) and electronic pairing correlations in moiré Hubbard systems with open boundaries. By introducing channel-selective non-reciprocity in the hopping terms, the authors demonstrate that NHSE-induced localization strongly amplifies boundary local density of states (LDOS), leading to a non-monotonic "golden window" of enhanced pairing susceptibility, particularly within $y \in [0.5, 1.2]t$. Through exact diagonalization and non-Hermitian DMRG calculations, the paper establishes robust enhancement in onsite pairing correlations—distinct from trivial density redistribution—while concurrently suppressing competing antiferromagnetic channels. The results yield dome-shaped $T_c(y)$ fingerprints and outline clear experimental signatures for coherent-driven versus reservoir-dominated regimes.

Model and Methodology

The underlying model is a triangular moiré superlattice described by a non-Hermitian extension of the Hubbard Hamiltonian, featuring asymmetric hopping ($t+y$/$t-y$) in one direction (Hatano-Nelson protocol), with on-site Hubbard interaction parameter $U/t$ spanning 0 to 12. The study focuses on half-filling and mostly 3×3 clusters, leveraging exact diagonalization with right-eigenstate observables, as well as biorthogonal checks and non-Hermitian DMRG (NH-DMRG) for larger clusters. Observables include double occupancy $D$, pairing susceptibility $\chi_{\text{SC}}$, and skin order $S$.

Physical Mechanisms and Results

Skin Effect Reshaping Moiré Bands

Switching from periodic to open boundaries triggers NHSE: eigenstates collapse exponentially toward one boundary, quantified by penetration depth $\lambda_{\text{skin}}\sim 1/\ln[(t+y)/(t-y)]$. Even moderate $y\sim0.1t$ dramatically localizes modes in the originally flat moiré band, compressing the spectrum and boosting boundary LDOS by several orders of magnitude ($T_c(y)$0).

Golden Window of Enhanced Pairing

Pairing enhancement via NHSE is non-monotonic. For intermediate non-reciprocity ("golden window," $T_c(y)$1), double occupancy $T_c(y)$2 peaks at up to +21% over the Hermitian baseline, then declines as over-localization suppresses response. Channel-selective decomposition shows onsite pairing grows ($T_c(y)$3), while the competing negative off-site antiferromagnetic correlations shrink ($T_c(y)$4). Total pairing susceptibility nearly doubles ($T_c(y)$5 relative to $T_c(y)$6).

Key statistical findings:

• Peak enhancement at $T_c(y)$7 ($T_c(y)$8), with +6–14% at stronger $T_c(y)$9.
• Magnitude of enhancement decreases in larger clusters but persists—finite-size scaling extrapolates robust enhancement ($t+y$0) in the thermodynamic limit.

The enhancement mechanism is fundamentally many-body. Comparing non-interacting ($t+y$1) baselines shows smaller effects with no over-localization collapse, ruling out simple density redistribution.

Channel Selectivity and Competing Orders

The NHSE acts channel-selectively: it promotes onsite Cooper pairing while suppressing competing AFM order. No evidence for actual magnetic ordering or phase separation is found across studied clusters, confirming selectivity. The mechanism is robust across lattice geometries (triangular, square, honeycomb), particle-hole symmetry, and disorder.

Boundary Condition and Universality

Under periodic boundary conditions, NHSE is absent and the non-monotonic peak vanishes; only weak monotonic density-of-states effects or emergent Hermiticity remain. The enhancement, and its dependence on open boundaries, is universal and tied to the NHSE mechanism.

Topological Signatures

The single-particle spectrum exhibits a non-Hermitian winding number $t+y$2 for $t+y$3 in PBC, reflecting spectral winding in the complex plane. However, the study does not claim many-body topological order; future analyses with larger clusters are suggested.

Experimental Relevance and Signatures

The predicted enhancement can be probed in twisted transition-metal dichalcogenide (tTMD) heterostructures (e.g., tWSe$t+y$4) and cold-atom platforms. Distinct mechanisms for NHSE induction—coherent lattice modulation vs. dissipative reservoir coupling—are expected to yield qualitatively different pairing responses: a full non-monotonic dome for coherent drives, monotonic enhancement for reservoirs. Gate-tunable non-reciprocal transport, edge LDOS enhancement in STM, and route-dependent pairing fingerprints are outlined as experimental tests.

Theoretical Implications and Future Directions

The NHSE introduces a previously unrecognized mechanism for localized pairing enhancement in correlated electron systems, driven by boundary LDOS amplification rather than global density redistribution or Fermi-velocity reduction. This response is distinct from single-particle NHSE and cannot be captured by mean-field or non-interacting approximations. The findings suggest the possibility of engineering boundary-driven superconductivity in moiré platforms through controlled non-reciprocal hopping. Future directions include tensor-network approaches for larger clusters, exploring bulk long-range order, and connection to Chern-band pairing proposals in twisted TMD and moiré graphene systems.

Conclusion

This study demonstrates that the NHSE in open-boundary moiré Hubbard systems generates a robust, channel-selective enhancement in pairing susceptibility within an intermediate "golden window" of non-reciprocity. The enhancement is genuine and many-body, surviving finite-size scaling and various lattice geometries, while showing clear dependence on boundary conditions. The mechanism provides a new paradigm for manipulating superconducting tendencies via non-Hermitian engineering, with experimentally testable predictions and strong implications for correlated-electron physics in moiré materials (2606.20425).