Bibliographic record
Abstract
Electronic states in band insulators and semimetals can form nontrivial topological structures which can be classified by introducing a set of well defined topological invariants. There are interesting experimentally observable phenomena tied to these topological invariants which are robust as long as the invariants remain well-defined. One important class manifesting these topological phenomena in the bulk and at the edges is the time reversal invariant topological band insulators first discovered in HgTe in 2007. Since then, there have been enormous efforts from both the experimental and the theoretical sides to discover new topological materials and explore their robust physical signatures. In this thesis, we study one important aspect, i.e., the electromagnetic response in the bulk and at the spatial boundaries. First we show how the topological action, which arises in a time reversal invariant three dimensional band insulator with nontrivial topology, is quantized for open and periodic boundary conditions. This confirms the Z2 nature of the strong topological invariant required to classify time-reversal invariant insulators. Next, we introduce an experimentally observable signature in the response of electronic spins on the surface of these materials to the perpendicular magnetic field. We proceed by considering electromagnetic response in the bulk of topological Weyl semimetals in a systematic way by considering a lattice model and we address important questions on the existence or absence of the Chiral anomaly. In the end, we show how a topological phase in a one dimensional system can be an energetically favourable state of matter and introduce the notion of self-organized topological state by proposing an experimentally feasible setup.
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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 | 0.000 |
| 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 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".