Impurities Induce Localisation Without a Characteristic Scale in Lattices

Scientists Hui Liu and Zhihao Xu of Shanxi University have detailed how imperfections within a novel lattice structure acutely influence energy dissipation. Anomalous scale-free localization and associated loss bursts occur within a non-Hermitian dissipative lattice, as demonstrated by Liu and colleagues. Strategically placed impurities function as tunable boundaries, controlling energy spread and loss from the system. The research links this unique localization type with enhanced dissipation, potentially offering new ways to manipulate energy flow in non-Hermitian lattices without traditional gap closing methods.

Impurity-induced energy dissipation in a non-Hermitian cross-stitch lattice

The long-time integrated dissipation probability increased fivefold near deliberately placed impurities, a result previously unattainable without inducing imaginary-gap closing. At Shanxi University, researchers observed this impurity-induced loss burst within a non-Hermitian dissipative cross-stitch lattice, revealing a mechanism where imperfections act as tunable boundaries controlling energy dissipation. This effect, analogous to edge bursts but occurring in the bulk of the lattice, relies on anomalous scale-free localization, where the strength of energy trapping varies depending on the energy of each eigenstate. Non-Hermitian systems, unlike their Hermitian counterparts, do not adhere to the principle of energy conservation, allowing for phenomena like dissipation and gain, and are increasingly studied for their potential in novel device applications. The cross-stitch lattice, a specific type of photonic crystal, is designed with a unique geometry intended to enhance these non-Hermitian effects. Dissipation, in this context, refers to the irreversible loss of energy from the system, typically through mechanisms like absorption or radiation.

Multiple impurities each create a similar local dissipation region; however, the strongest burst ultimately depends on the initial position of the energy wave and the direction of non-reciprocal drift within the lattice. Dissipation enhancement extends to regions encompassing the impurity site and its immediate neighbour, demonstrating a localized burst effect. This localization is not uniform across all energies; the Lyapunov exponent, governing localization, varied with the energy of each eigenstate, meaning different energy levels localize with differing strengths, a phenomenon termed anomalous scale-free localization. This scale-free behaviour is crucial, as it indicates that the localization strength doesn’t follow a simple pattern with energy, offering a greater degree of control. Spectral loops remained clearly separated from the real-energy axis throughout the experiments, bypassing the need for imaginary-gap closing, a common technique used to induce these effects. Imaginary-gap closing typically involves modifying the lattice to create energy states with imaginary energies, which can lead to instability and uncontrolled dissipation. Avoiding this allows for a more stable and predictable manipulation of energy flow. While these findings demonstrate precise control over energy dissipation, translating this to practical devices requires overcoming challenges in maintaining the necessary precision in lattice construction and impurity placement. Fabrication tolerances and material imperfections could significantly impact the observed effects.

Local basis rotation and tunable boundaries induce scale-free localisation

A key technique enabling these observations involved a local basis rotation, effectively transforming the complex cross-stitch lattice into a more manageable form. This mathematical manipulation mapped the original system onto an effective non-Hermitian Su-Schrieffer-Heeger (SSH) lattice, simplifying analysis. The SSH lattice is a well-studied model in condensed matter physics, known for its topological properties and edge states. By mapping the cross-stitch lattice onto this simpler model, researchers could leverage existing theoretical tools and understanding. Consequently, deliberately placed impurities could be treated as tunable boundaries, controlling energy flow within the lattice; these impurities function like adjustable gates in a complex circuit, directing where energy can and cannot travel. The concept of tunable boundaries is central to this research, allowing for dynamic control over energy localization and dissipation.

Carefully adjusting the strength of these ‘gates’ allowed scientists to explore how energy becomes trapped, a phenomenon known as scale-free localization, and how this impacts the overall dissipation of energy from the system. Investigations of energy behaviour within a cross-stitch lattice varied the impurity strength, denoted by η, to explore different boundary conditions and observe how energy becomes trapped via scale-free localization. The impurity-free periodic-boundary-condition point is at η = 1. By systematically varying η, the researchers could effectively ‘tune’ the boundaries created by the impurities, transitioning between different regimes of energy confinement. This process differs from typical impurity-induced localization due to its dependence on energy levels, providing a more nuanced understanding of energy confinement. Traditional impurity-induced localization often results in a broad, energy-independent suppression of transmission, whereas the observed scale-free localization exhibits a more complex energy dependence. The ability to control localization on an energy-specific basis opens up possibilities for designing filters and other energy-selective devices.

Tunable energy flow achieved via strategically engineered material imperfections

Controlling energy dissipation within materials is vital for designing more efficient devices, but achieving precise control has traditionally demanded complex manipulation of a material’s fundamental properties. This often involves altering the material’s composition, crystal structure, or dimensionality. Despite acknowledging concerns about the complexity of these ‘cross-stitch’ lattices, artificial structures not easily replicated in nature, this work demonstrates an important principle. The creation of such lattices requires advanced fabrication techniques, such as nanofabrication and 3D printing, which present significant engineering challenges. This offers a new pathway for designing more efficient electronics and photonics, potentially reducing energy loss in devices. Reducing energy loss is crucial for improving the performance and reducing the operating costs of electronic and photonic devices.

This work details how imperfections within a specifically engineered lattice can dramatically alter energy dissipation, bypassing the need for previously required complex material adjustments. Anomalous scale-free localization was linked to impurity-induced loss bursts, concentrating energy dissipation at specific points within the lattice. The lattice remained stable while energy behaviour changed, demonstrating a major advancement over techniques requiring imaginary-gap closing. This stability is essential for practical applications, as it ensures that the device operates reliably over time. The ability to manipulate energy dissipation without resorting to unstable or complex material modifications represents a significant step towards realising more efficient and robust devices. Further research will focus on exploring the limits of this control and investigating the potential for integrating this principle into functional devices.

The research identified anomalous scale-free localization and associated loss bursts within a non-Hermitian dissipative cross-stitch lattice. This demonstrates that energy dissipation can be controlled by strategically introducing imperfections into the material’s structure, rather than altering its fundamental properties. The observed localization concentrates energy loss at specific points, offering a new method for managing energy flow in materials. Researchers found this effect occurred without compromising the lattice’s stability, and plan to explore integrating this principle into functional devices.