Symmetry-protected Bipolar Skin Effect Survives Moderate Disorder before Hierarchical Breakdown in Non-Hermitian Systems

The behaviour of open physical systems, those that exchange energy with their surroundings, presents a significant challenge to conventional understanding, particularly when combined with inherent disorder. Ali Tozar from Hatay Mustafa Kemal University and colleagues now reveal a surprising level of robustness in these systems, uncovering a unique ‘bipolar skin effect’ within a non-Hermitian chain exhibiting spin-orbit coupling. This effect causes electron states with different spin to localise at opposite edges of the material, and the research demonstrates that this symmetry-protected arrangement persists even with considerable disorder, unlike previous expectations. By meticulously mapping the system’s behaviour, the team establishes a new regime of disorder-resistant non-reciprocity, distinct from both simple material properties and complete electron immobilisation, and offers crucial insight into the fundamental physics of open, disordered systems.

Disorder’s influence on topological phases, particularly when spin-orbit coupling is present, remains incompletely understood. This research uncovers a Z2 topological bipolar skin effect within a non-Hermitian Rashba chain, where spin-up and spin-down electrons localize at opposite boundaries. The team rigorously computes Lyapunov exponents and introduces a biorthogonal spin-separation index to map the global phase diagram, revealing a hierarchical breakdown of topology. Results demonstrate that the Z2 skin effect remains protected against moderate disorder, but collapses into a trivial skin phase before the onset of Anderson localization, establishing a distinct regime of disorder-robust topological non-reciprocity, distinguishing it from previously known behaviours.

Rashba Chain Disorder and Z2 Skin Effect

Scientists investigated the interplay between non-Hermitian physics and disorder in a Rashba chain, a system exhibiting strong spin-orbit coupling. The study pioneered a method to map the global phase diagram of this system, revealing a unique Z₂ bipolar skin effect where spin-up and spin-down states localize at opposite boundaries. To characterize the system’s behavior, researchers employed the transfer matrix approach, adapting it to precisely compute the Lyapunov exponent, a measure of state localization, and rigorously account for numerical instabilities inherent in non-Hermitian systems. This implementation built upon previously established robust scaling frameworks.

The team developed a bi-orthogonal formulation to probe the topological nature of the delocalized phase, projecting the system’s wavefunctions onto a bi-orthogonal basis. This allowed them to define a spin separation index, quantifying the spatial segregation of spin modes, calculated using left and right eigenvectors to accurately capture skin accumulation. The index serves as an order parameter for the Z₂ skin phase, distinguishing it from trivial delocalization. Researchers then systematically varied both the strength of spin-orbit coupling and the degree of disorder to establish the global phase structure, identifying a broad delocalized regime separated from an Anderson localized phase by a sharp boundary defined by the Lyapunov exponent equaling zero.

To confirm the topological origin of the observed spin separation, scientists performed control calculations under both open and periodic boundary conditions. Under periodic boundaries, the spin separation index vanished, demonstrating that the effect originates from non-trivial point-gap topology rather than bulk polarization. The team further illuminated this interplay by superimposing topological isosurfaces onto the mobility edge, revealing that the Z₂ topological phase is a proper subset of the delocalized regime. This allowed them to identify a critical disorder strength, at which topological protection collapses, a value strictly smaller than the threshold for Anderson localization, demonstrating a hierarchical breakdown of the system’s properties.

Spin Separation and Robust Topological Skin Effect

Scientists have discovered a robust topological state in a non-Hermitian Rashba chain, revealing a Z2 bipolar skin effect where spin-up and spin-down electrons localize at opposite boundaries of the material. This work establishes a distinct phase of matter characterized by the spatial separation of spin, opening avenues for novel spintronic devices. The research team rigorously mapped the global phase diagram of the system, revealing a hierarchical breakdown of topology as disorder increases. The study employed a one-dimensional tight-binding chain with open boundary conditions, governed by a non-Hermitian Hamiltonian incorporating spin-orbit coupling and non-reciprocal hopping.

Researchers constructed the model to rigorously investigate the interplay between spin-orbit coupling and the skin effect, utilizing spin-dependent amplification factors within the hopping matrices. By computing the Lyapunov exponent, the team identified the mobility edge separating localized and extended states. The numerical implementation strictly followed established protocols for handling non-Hermitian instabilities and finite-size scaling, ensuring robust results. Results demonstrate a broad delocalized regime at weak disorder, clearly separated from the Anderson localized phase by a sharp boundary.

The team established that the Z2 symmetry protects the bipolar skin effect against moderate disorder, preventing the decoupling of spin channels. To probe the topological nature of the delocalized phase, scientists employed a bi-orthogonal formulation and defined a spin separation index, quantifying the spatial segregation of spin modes. Measurements of this index serve as an order parameter for the Z2 skin phase, clearly distinguishing it from trivial delocalization. The research establishes a distinct regime of disorder-robust topological non-reciprocity, distinguishable from both the trivial bulk limit and the Anderson localized phase, and provides a foundation for exploring novel quantum phenomena in non-Hermitian systems.

Rashba Lobe Survives Strong Disorder Effects

This research demonstrates a surprising resilience of non-Hermitian topological effects in the presence of significant disorder, challenging the conventional expectation that disorder always destroys such phenomena. Scientists uncovered a distinct phase, termed the “Rashba Lobe”, within a non-Hermitian Rashba chain where a bipolar skin effect, manifesting as localized states for different spin orientations at opposite boundaries, persists despite considerable randomness in the system. The team established that this effect is protected by a fundamental symmetry known as symplectic symmetry, remaining stable up to a critical level of disorder before transitioning to a trivial state. The investigation involved a rigorous methodological framework, moving beyond standard spectral analysis to employ bi-orthogonally projected spin metrics and Lyapunov exponents, which allowed researchers to disentangle the complex interplay between non-reciprocity, spin-orbit coupling, and disorder.

This approach successfully mapped the phase diagram and revealed a hierarchical breakdown of the skin effect as disorder increases. The findings suggest a new paradigm for designing quantum devices, moving away from the pursuit of perfect materials and instead embracing imperfections by leveraging symplectic symmetry to stabilize robust spin currents. This “Disorder-Harvesting Topology” offers a transformative path for next-generation spintronics and quantum technologies.