RECORD
Unconventional topological edge states in one-dimensional gapless systems stemming from nonisolated hypersurface singularities
Mesoscale and Nanoscale Physics · Submitted 5 Mar 2025
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Unexpectedly, such gapless systems still afford topologically protected edge states at system boundaries, challenging the conventional understanding based on band gaps.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Topologically protected edge states have been extensively studied in systems characterized by the topological invariants in band gaps (also called line gaps). In this study, we unveil a whole new form of edge states that transcends the established paradigms of band-gap topology. In contrast to the traditional stable edge states in topological insulators with specific band gaps, the one-dimensional systems we investigate are inherently gapless with the Brillouin zones being mapped to the loops encircling hypersurface singularities in a higher-dimensional space with parity-time symmetry. These hypersurface singularities are nonisolated degeneracies embedded entirely on exceptional surfaces, rendering the energy gaps in our systems inevitably closed at the intersections of the Brillouin zone loop and the exceptional surfaces. Unexpectedly, such gapless systems still afford topologically protected edge states at system boundaries, challenging the conventional understanding based on band gaps. To elucidate the existence of these edge states in the absence of a band-gap-based invariant, we propose a theoretical framework based on eigen-frame rotation and deformation that incorporates non-Bloch band theory. Finally, we experimentally demonstrate this new form of topological edge states with nonreciprocal circuits for the first time. Our work constitutes a major advance that extends topological edge states from gapped phases to gapless phases, offering new insights into topological phenomena.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Topologically protected edge states have been extensively studied in systems characterized by the topological invariants in band gaps (also called line gaps). | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | In this study, we unveil a whole new form of edge states that transcends the established paradigms of band-gap topology. | contribution 0.97 | 0.91 | 0.23 | asserted 1.00 |
| s2 | In contrast to the traditional stable edge states in topological insulators with specific band gaps, the one-dimensional systems we investigate are inherently gapless with the Brillouin zones being mapped to the loops encircling hypersurface singularities in a higher-dimensional space with parity-time symmetry. | contribution 0.92 | 0.68 | 0.09 | asserted 1.00 |
| s3 | These hypersurface singularities are nonisolated degeneracies embedded entirely on exceptional surfaces, rendering the energy gaps in our systems inevitably closed at the intersections of the Brillouin zone loop and the exceptional surfaces. | result 0.39 | 0.70 | 0.06 | asserted 1.00 |
| s4 | Unexpectedly, such gapless systems still afford topologically protected edge states at system boundaries, challenging the conventional understanding based on band gaps. | result 0.95 | 0.84 | 0.62 | asserted 1.00 |
| s5 | To elucidate the existence of these edge states in the absence of a band-gap-based invariant, we propose a theoretical framework based on eigen-frame rotation and deformation that incorporates non-Bloch band theory. | method 0.87 | 0.91 | 0.06 | asserted 0.98 |
| s6 | Finally, we experimentally demonstrate this new form of topological edge states with nonreciprocal circuits for the first time. | contribution 0.65 | 0.97 | 0.13 | asserted 1.00 |
| s7 | Our work constitutes a major advance that extends topological edge states from gapped phases to gapless phases, offering new insights into topological phenomena. | interpretation 0.87 | 0.71 | 0.73 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Topologically protected edge states have been extensively studied in systems characterized by the topological invariants in band gaps (also called line gaps). In this study, we unveil a whole new form of edge states that transcends the established paradigms of band-gap topology. In contrast to the traditional stable edge states in topological insulators with specific band gaps, the one-dimensional systems we investigate are inherently gapless with the Brillouin zones being mapped to the loops encircling hypersurface singularities in a higher-dimensional space with parity-time symmetry. These hypersurface singularities are nonisolated degeneracies embedded entirely on exceptional surfaces, rendering the energy gaps in our systems inevitably closed at the intersections of the Brillouin zone loop and the exceptional surfaces. Unexpectedly, such gapless systems still afford topologically protected edge states at system boundaries, challenging the conventional understanding based on band gaps. To elucidate the existence of these edge states in the absence of a band-gap-based invariant, we propose a theoretical framework based on eigen-frame rotation and deformation that incorporates non-Bloch band theory. Finally, we experimentally demonstrate this new form of topological edge states with nonreciprocal circuits for the first time. Our work constitutes a major advance that extends topological edge states from gapped phases to gapless phases, offering new insights into topological phenomena.
Human review
How the literature uses it
1 arXiv paper cite this in 1 sentence
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.