[Paper Review] Observation of non-Hermitian topology and its bulk-edge correspondence

Ananya Ghatak, Martin Brandenbourger+2 more|arXiv (Cornell University)|Jul 26, 2019

Quantum Mechanics and Non-Hermitian Physics33 citations

TL;DR

This study experimentally demonstrates a novel bulk-edge correspondence in non-Hermitian topological systems using a mechanical metamaterial, showing that a change in the non-Hermitian topological invariant directly corresponds to a shift in localization of topological edge modes. The work confirms robust edge mode behavior in non-Hermitian systems via a quantum-to-classical analogy, advancing the understanding of non-Hermitian topology and enabling new wave manipulation strategies in metamaterials.

ABSTRACT

Over the last few years, topological edge modes -- excitations that are localized at the materials' edges, yet that are characterized by a topological invariant defined from the material's bulk -- have enabled the creation of robust electronic, electromagnetic and mechanical transport properties across a wide range of systems, from cold atoms to metamaterials and geophysical flows. The advent of non-Hermitian topological systems -- wherein energy is not conserved -- has sparked considerable theoretical advances. In particular, novel topological phases that can only exist in non-Hermitian systems have been introduced. However, what are the properties of such phases and whether they can be observed have remained open questions. Here, we discover and observe experimentally a novel form of bulk-edge correspondence of a one-dimensional system characterized by a non-Hermitian topological phase. Namely, we find that a change in the non-Hermitian topological invariant corresponds to a change of localization of the topological edge mode. Using a quantum-to-classical analogy, we create a mechanical metamaterial with suitably designed interactions, where we observe experimentally the predicted bulk-edge correspondence, which in turn demonstrates the robustness of our findings. Our work sheds light on the nascent field of non-Hermitian topology and boosts metamaterials by opening new avenues to manipulate waves in unprecedented fashions.

Motivation & Objective

• To investigate the properties of non-Hermitian topological phases, which lack energy conservation and were previously unobserved experimentally.
• To determine whether non-Hermitian topological invariants can lead to robust edge modes with distinct localization behavior.
• To establish a bulk-edge correspondence in non-Hermitian systems, where topological invariants in the bulk dictate edge mode localization.
• To validate theoretical predictions of non-Hermitian topology through a controllable mechanical metamaterial platform.

Proposed method

• A mechanical metamaterial with tailored non-Hermitian interactions was designed to emulate quantum non-Hermitian systems via a quantum-to-classical analogy.
• The system's Hamiltonian was engineered to support non-Hermitian topological phases with tunable gain and loss, enabling control over edge mode localization.
• Edge modes were experimentally probed by measuring displacement responses under localized excitation, revealing localization shifts across phase boundaries.
• The non-Hermitian topological invariant was computed from the bulk band structure, linking it to the observed edge mode behavior.
• Systematic variation of coupling parameters allowed tuning between different topological phases, enabling direct observation of the correspondence.

Experimental results

Research questions

• RQ1 How does the non-Hermitian topological invariant influence the localization of edge modes in a one-dimensional system?
• RQ2 Can a bulk-edge correspondence exist in non-Hermitian systems, and if so, how is it experimentally observable?
• RQ3 What are the physical signatures of non-Hermitian topological phases in a classical mechanical metamaterial?
• RQ4 How does the localization of topological edge modes change across a topological phase transition in non-Hermitian systems?
• RQ5 To what extent are the observed edge modes robust against disorder or perturbations in non-Hermitian systems?

Key findings

• A direct correspondence was observed between changes in the non-Hermitian topological invariant and shifts in the localization of topological edge modes in the mechanical metamaterial.
• The edge modes exhibited distinct localization behavior—either at one end or the other—depending on the topological phase, confirming the predicted bulk-edge correspondence.
• The experimental system successfully realized a non-Hermitian topological phase with robust edge modes, validating theoretical predictions.
• The quantum-to-classical analogy enabled reliable experimental access to non-Hermitian topology, demonstrating its feasibility in classical systems.
• The findings confirm that non-Hermitian systems support unique topological phases not possible in Hermitian systems, with measurable and robust physical signatures.