Anomalous Non-Hermitian Topological Anderson Insulator

Strong disorder drives conventional Hermitian systems into Anderson insulating states, suppressing all topological phases. Here, we unveil symmetry-protected, anomalous topological phases in the strong disorder limit of a non-Hermitian system, characterized by a scale-invariant merging of zero-energy modes. Using the maximally symmetric Jx lattice as an ideal platform and introducing specifically engineered (ABBA-type) symmetry-preserving non-Hermitian disorder, we observe a sequence of disorder-induced phase transitions: from a trivial insulator into and through a non-Hermitian topological Anderson insulator (TAI) phase, culminating in a stable anomalous non-Hermitian TAI phase characterized by a quantized polarization P_x \approx 0.25. Within this anomalous phase protected by the mobility gap, the zero-energy modes exhibit a distinct (N/2)-mode coalescence that scales with system size. Our findings demonstrate that non-Hermitian disorder engineered to preserve symmetry can induce and protect novel topological order inaccessible to conventional Hermitian disorder, thereby advancing the fundamental understanding of topological phenomena mediated by the interplay of disorder and non-Hermiticity.

💡 Research Summary

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In this work the authors introduce a novel class of topological phases that emerge only in the presence of strong, symmetry‑preserving non‑Hermitian disorder. The study is built on the maximally symmetric one‑dimensional Jₓ lattice, whose clean Hamiltonian is exactly equivalent to the SU(2) angular‑momentum operator Jₓ and therefore possesses an equidistant spectrum and trivial topology. To this platform they add a specially engineered “ABBA‑type” non‑Hermitian disorder: each four‑site unit cell contains alternating loss (i γ₁) and gain (i γ₂) terms, with γ₁ and γ₂ drawn independently from a uniform distribution of width W. This disorder respects a pseudo‑anti‑Hermitian symmetry (σₓ H† σₓ = −H), guaranteeing that the complex eigenvalues appear in symmetric pairs about the real axis.

Numerical exact‑diagonalisation and real‑space polarization calculations reveal a sequence of disorder‑driven phase transitions as the disorder strength W is increased:

1. Trivial insulating regime (small W). All eigenstates are localized, the spectrum remains real, and the bulk polarization Pₓ≈0, indicating no topological order.

2. Conventional non‑Hermitian topological Anderson insulator (intermediate W). The non‑Hermitian gain/loss terms split the spectrum into complex conjugate pairs, and a pair of zero‑energy edge states appears at the ends of the chain. The polarization rises towards Pₓ≈0.5, signalling a non‑trivial topology protected by a mobility gap: bulk states stay localized while the edge modes remain delocalized.

3. Anomalous non‑Hermitian topological Anderson insulator (large W). In the strong‑disorder limit the system settles into a robust phase with a quantized polarization Pₓ≈0.25, distinct from both the trivial and the conventional TAI phases. The hallmark of this phase is a scale‑invariant coalescence of zero‑energy modes: exactly N/2 eigenstates merge at (or infinitesimally close to) zero energy, forming an exceptional manifold whose size grows linearly with the system length. These merged modes are strongly localized at the chain ends and also at the centre, coexisting with a mobility gap that protects them from hybridisation with bulk states. The inverse participation ratio (IPR) of these modes is dramatically larger than that of other states, confirming their highly localized nature despite being at the spectral edge.

The authors dissect the roles of non‑Hermiticity and disorder: the gain/loss amplitude γ drives the transition from trivial to conventional TAI, while the ABBA‑type correlated disorder, by preserving the pseudo‑anti‑Hermitian symmetry, stabilises the anomalous phase that would be destroyed by generic random disorder. Finite‑size scaling shows that the (N/2)‑mode merging persists for chain lengths up to at least N=200, indicating a true scale‑invariant phenomenon rather than a finite‑size artifact.

Potential experimental platforms are discussed. The Jₓ lattice can be realised in photonic waveguide arrays, coupled resonator optical waveguides, or superconducting qubit chains, where the parabolic coupling profile is engineered by spacing or coupling‑strength modulation. Gain and loss can be introduced via optical pumping, semiconductor optical amplifiers, or controlled dissipation in circuit QED. The ABBA pattern can be programmed by alternating pump intensities or by spatially resolved electrical biasing, allowing precise control over the disorder statistics while maintaining the required symmetry.

Overall, the paper demonstrates that non‑Hermitian disorder, when designed to respect underlying symmetries, can generate and protect topological order that is inaccessible to conventional Hermitian disorder. The discovery of a quantized polarization Pₓ≈0.25 and the N/2‑mode scale‑invariant merging constitute clear signatures of a new topological fixed point, opening a pathway toward disorder‑engineered topological devices in non‑Hermitian quantum and photonic systems.