Multi-topological phases of matter
Bibliographic record
Abstract
The discovery of topological phases of matter and topological boundary states had tremendous impact on condensed matter physics and photonics, where topological phases are defined via energy bands, giving rise to topological band theory. However, topological systems that cannot be described by band topology but still support non-trivial boundary states are little-known and largely unexplored. Here, we uncover a new kind of topological phase of matter named "multi-topological phase" (MTP) that features multiple sets of boundary states, where each set is associated with one distinct topological invariant. Unlike conventional topological phase transitions, the MTP transitions can occur without band-gap closing. We present typical examples of MTPs in a one-dimensional topological insulator and a two-dimensional higher-order topological insulator, where the systems are otherwise trivial according to band topology. Furthermore, MTPs can exist also in indirectly gapped Chern insulators, beyond the regime where the conventional bulk-boundary correspondence predicts the existence of boundary states. Experimentally, we demonstrate the first two examples of MTPs in laser-written photonic lattices. Our findings constitute a fundamental advance in topological physics and provide a route for designing novel topological materials.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".