[論文レビュー] Edge-controlled non-Hermitian skin effect in the modified Haldane model

Nobuhiro Ito, Shun Uchino|arXiv (Cornell University)|Mar 2, 2026

Quantum Mechanics and Non-Hermitian Physics被引用数 0

ひとこと要約

The paper shows edge-localized gain/loss in a modified Haldane nanoribbon induces non-Hermitian skin effects, including a nonlocal antichiral skin effect, with PT symmetry governing bulk NHSE viability.

ABSTRACT

The hybrid skin-topological effect (HSTE) arises from the interplay between the non-Hermitian skin modes and topologically protected edge states. Here, we investigate the HSTE associated with antichiral edge states in a modified Haldane nanoribbon with gain and loss applied exclusively at the zigzag edges. We show that in antichiral systems, the HSTE originates from an imbalance of effective gain and loss between edge states and counter-propagating bulk modes, revealing a mechanism distinct from that in conventional chiral systems. Remarkably, in sufficiently narrow ribbons, gain or loss applied to only one edge induces a skin effect in the states localized at the opposite edge, demonstrating a non-Hermitian nonlocal antichiral skin effect. We further show that edge-localized dissipation can induce bulk skin modes only when $\mathcal{PT}$ symmetry is broken, while the bulk non-Hermitian skin effect is strictly forbidden in the $\mathcal{PT}$-symmetric regime. By tuning the gain and loss applied solely at the edges, both the emergence and localization direction of bulk skin modes can be controlled. Our results establish a symmetry-based mechanism for controlling non-Hermitian skin effects via edge dissipation in antichiral systems.

研究の動機と目的

• Motivate study of non-Hermitian skin effects (NHSE) arising from edge dissipation in topological systems.
• Investigate hybrid skin–topological effects (HSTE) for antichiral edge states in a modified Haldane model.
• Identify how edge-localized gain/loss affects edge and bulk states under different PT-symmetric conditions.
• Elucidate mechanisms leading to a nonlocal NHSE and its dependence on system width and PT symmetry.

提案手法

• Employ a modified Haldane nanoribbon with imaginary on-site potentials iγ1 and iγ2 on the lower and upper zigzag edges.
• Analyze the effective Hamiltonian including NN and NNN hoppings with a phase φ in the NNN term.
• Characterize PT symmetry via H(γ1, γ2) and derive the condition γ1 = −γ2 for PT symmetry.
• Compute spectra under periodic and open boundary conditions along x to identify NHSE manifestations.
• Define and use edge localization metric S to quantify edge vs bulk localization.
• Discuss the concept of effective gain/loss γeff to explain edge-bulk coupling and NHSE.
• Map phase diagram in the (γ1, γ2) plane showing PT-symmetric and PT-broken regimes and bulk NHSE behavior.

実験結果

リサーチクエスチョン

• RQ1 Does edge-localized dissipation induce NHSE in a system with antichiral edge states?
• RQ2 How does PT symmetry (or its breaking) control bulk NHSE and the emergence/localization of skin modes?
• RQ3 What is the mechanism of NHSE for antichiral edge states compared to chiral edge states?
• RQ4 Can edge gain/loss produce nonlocal NHSE affecting opposite edges or bulk states?
• RQ5 How do system width and boundary conditions influence the presence and direction of NHSE?

主な発見

• In the PT-symmetric case (γ1 = −γ2), only antichiral edge states exhibit NHSE while bulk states remain PT-symmetric and extended.
• When PT symmetry is broken (e.g., γ1 = −0.6, γ2 = 0 or γ1 = 0, γ2 = +0.6), both edge and bulk states develop NHSE, and a nonlocal antichiral skin effect appears where the opposite edge shows localization.
• Edge localization direction matches winding numbers: lower-edge states localize to the left and upper-edge states to the right under open boundaries in the studied setups.
• Bulk NHSE is forbidden in the PT-symmetric regime because bulk energies remain real and no point gap opens; it emerges only after PT symmetry breaking.
• By tuning edge gain/loss, both emergence and localization direction of bulk skin modes can be controlled, with a phase-diagram separating two bulk-skin phases related by PT symmetry.
• The mechanism for HSTE in antichiral systems relies on an imbalance between edge-state and counter-propagating bulk-state gain/loss, distinct from chiral-edge-based HSTE.