Rim to sub-symmetric topology phase protection

June 08, 2023

(Nanowerk News) An international team led by researchers at the University of Nankai in China and at the University of Zagreb in Croatia, together with a team at the Institut national de la recherche scientifique (INRS) in Canada, led by Roberto Morandotti have made important breakthroughs in the study of phase topology.

Their findings were recently published in Natural Physics (“Sub-symmetry protected topology conditions”).

In the last decade, topological photonics has attracted increasing attention because of the unique prospect of achieving high-performance light manipulation in terms of robustness and stability. Discoveries in topological photonics have paved the way for the development of a new generation of photonic devices, such as lasers and topological cavities, featuring a topologically protected state that is immune to interference and defects.

The concept of topology in physics is inherited from mathematics, where topology is used to study the geometrical properties of an object regarding the quantity retained under continuous deformation. Two objects are topologically identical when the surface of one can continuously deform into the other and vice versa, for example, a coffee cup and a torus are equivalent from a topological point of view.

In physics, the concept of topology is used to describe the characteristics of energy bands, leading to the prediction of new topological states of matter and various topological materials. The different topological phases (trivial and nontrivial) are differentiated by introducing a precisely quantized topological invariant, which allows establishing a relationship between bulk properties and feature appearance at these material boundaries, known as the “bulk-boundary correspondence”. In this respect, the most distinctive feature of a nontrivial topology is the presence of strong topological boundary states protected by certain spatial and/or intrinsic symmetries. Schematic illustration classifying faults in a symmetry protected topology phase (SPT phase). Overlapping regions surrounded by red, gray, and green lines represent symmetry-protected topological phases that display topological invariants and corresponding topological boundary states. The gray line is a set of perturbations that affect the boundary state but do not impair the topological invariance of the entire system. The red and green line areas indicate the boundary states protected by their respective associated sub-symmetries. The illustrated example shows two perturbation sets that satisfy the sub-symmetry but destroy the topological invariance of the whole system. In this case, the sub-symmetry protects the boundary state. (Image: Domenico Bongiovanni and coauthors)

In general, in a symmetry protected topological phase system (SPT phase), it is believed that a close relationship between topological boundary states, topological invariants, and one or more overall symmetries is indispensable to maintain topological protection against disturbances. As a result, neither topological invariants nor topological boundary states are irreparably affected by any distortion that breaks the underlying symmetry.

In this work, an international research team has challenged these traditional common beliefs, and thereby broadened the understanding of the SPT country boundaries. They found that even if the system no longer quantifies topological invariants and some kind of global symmetry, topological boundary states can still exist in the appropriate subspace, protected by what are called “sub-symmetries”.

“Our findings challenge the common notion of symmetry-protected topological phases in topologies and update the correspondence of topological invariants and boundary states”, said Domenico Bongiovanni one of the principal investigators, Postdoctoral researcher at INRS-EMT. “Our idea has the potential to explain the topological origin of many unconventional states and can find applications across multiple platforms and physical systems.”

The researchers, by introducing and exploring the concept of sub-symmetry, found that global symmetry in the traditional sense is not strictly necessary to protect topological boundary states. In this case, the topological boundary state is maintained as long as the symmetry of a particular subspace is satisfied, even when the overall topological invariant no longer exists.

The research team cleverly designed and fabricated photonic lattice structures using the cw-laser writing technique to satisfy the symmetry conditions of different subspaces. The experiment shows a proof of concept with the two most typical topological lattice: one-dimensional SSH and two-dimensional Kagome lattice.

In addition, the team innovatively introduced the concept of remote coupling symmetry into the Kagome lattice model, which resolved the current controversy about the existence and protection of high-level topology state topologies in the Kagome lattice.

This study not only challenges the traditional understanding of topological states protected by symmetry but also provides new ideas for research and application of topological states in different physical backgrounds. The impact of this work is expected to further promote the development of topological photonics and its cutting-edge interdisciplinary field, as well as the research and development of a new generation of topological photonic devices based on sub-symmetry protected boundary states.

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