Analytical solutions for domain walls within a non-Hermitian Su-Schrieffer-Heeger model have been derived by researchers from the Max Planck Institute for the Science of Light and National University of Singapore. These solutions extend studies beyond conventional skin modes to include finite-energy interface states that are separate from bulk energy levels, differing from previous investigations which focused on simpler interfaces with lower dimensionality. Joining different quantum materials creates new energy states within the combined structure.

Investigations now extend beyond simple one-dimensional systems to incorporate more intricate arrangements such as two-dimensional lattices, enabling greater control over wave behaviour within these engineered structures. The findings advance understanding of ‘non-Hermitian physics’, a field examining systems that do not follow conventional symmetry rules, revealing additional localised energies separate from typical bulk properties. Max Planck Institute for the Science of Light, Mengjie Yang and Flore K. Kunst have uncovered new energy states within joined quantum materials; these arise when combining substances creates unique properties not found individually.

The work builds on understanding ‘non-Hermitian physics’, exploring systems breaking conventional symmetry rules and revealing additional energies localised away from typical bulk behaviour. Consider shining light onto a surface and finding it concentrated at the edges rather than spread evenly; this illustrates the non-Hermitian skin effect observed in experiments. The team investigated how interfaces between engineered structures behave, considering both line-like (codimension one) and point-like (codimension two) boundaries, similar to drawing with lines or dots on paper.

Finite Energy Localised States Emerge in Non-Hermitian Domain Walls and Two-Dimensional Lattices

Analytical solutions reveal domain walls within a non-Hermitian Su-Schrieffer-Heeger model generate additional localised states at finite energy, an increase compared to earlier models predicting only zero-energy modes. These new states detach from the main band of energies under open boundary conditions where electrons are confined; this was previously unattainable with conventional approaches focused on simpler interfaces. The analysis extended beyond one dimension to investigate two-dimensional Lieb lattices exhibiting tunable funneling regimes towards boundaries of differing dimensions, allowing for greater control over electron behaviour and wave manipulation.

Exact diagonalization confirmed these analytical findings, revealing how changes in asymmetry influence state concentration at interfaces. Manipulating hopping parameters within the lattice allows for tunable regimes controlling the flow of energy toward both line and point defects, potentially enabling precise quantum state manipulation.

Two-dimensional Lieb lattices were also examined, displaying controllable funneling effects directing electrons toward boundaries of varying dimensionality, offering enhanced electronic behaviour and wave propagation control. This provides a pathway toward more efficient sensors and optical components as thorough mathematical mapping of energy behaviours within unusual materials lays a key foundation for future engineering efforts.

Symmetry exploitation streamlines solutions for non-Hermitian quantum models

Analytical derivation underpinned by symmetry-based assumptions unlocks solutions for complex quantum systems; this approach sidestepped computationally intensive methods struggling with these models. The non-Hermitian Su-Schrieffer-Heeger model, a simplified representation of alternating strong and weak bonds in a material, served as the starting point, where potential wave function shapes termed ‘ansatzes’ were carefully constructed guided by inherent system symmetries.

These ansatzes acted as educated guesses regarding electron behaviour across boundaries between different materials, dramatically reducing calculation complexity needed to find precise energy levels and distributions, akin to solving a puzzle through pre-assembly based on colour or shape instead of exhaustive combination attempts. The focus lay on analytical solutions for energy levels under open boundary conditions, meaning electrons are confined within the material rather than moving freely.

Mapping electron behaviour in non-Hermitian lattices reveals directional funneling regimes

Researchers increasingly focus on utilising the unusual properties of ‘non-Hermitian physics’, where materials break conventional symmetry rules offering new control over energy flow; this field promises advances in sensing and light manipulation but remains largely theoretical. Precise mathematical descriptions were extended beyond simple one-dimensional systems to investigate more complex two-dimensional lattices exhibiting “funneling regimes”, directing electrons towards boundaries. It is important to acknowledge that translating these findings from controlled simulations into practical devices requires further work, as understanding how electrons are directed toward material edges offers potential pathways for efficient sensors and optical components.

The team alongside collaborators, have demonstrated that interfaces between different quantum materials create entirely new energy states within a combined structure, distinct from energies typically found in either material alone. Their work reveals ‘domain walls’ support localised energies separate from those existing throughout bulk material; this contrasts with previous understandings largely focused on zero-energy modes confined to such boundaries, opening possibilities for greater control over electronic properties. These discoveries represent significant progress towards harnessing non-Hermitian physics for advanced technological applications, offering unprecedented opportunities in areas requiring precise manipulation of electron behaviour and wave propagation.

The research identified additional localised energy states generated by domain walls when combining two one-dimensional quantum materials exhibiting the non-Hermitian skin effect. This means that By gluing two Su-Schrieffer-Heeger chains with inverted coupling ratios together,. Researchers validated their analytical solutions using exact diagonalization and extended this interface construction to a two-dimensional Lieb lattice, observing controllable ‘funneling regimes’ directing electrons toward material boundaries. The findings offer greater understanding of how electronic properties can be controlled at interfaces between such materials.

👉 More information
🗞 Exact solutions of nonreciprocal Su-Schrieffer-Heeger model with domain walls
✍️ Tong Wang, Mengjie Yang and Flore K. Kunst
🧠 ArXiv: https://arxiv.org/abs/2609.17378

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