SciPost Submission Page
Hybrid symmetry class topological insulators
by Sanjib Kumar Das, Bitan Roy
Submission summary
| Authors (as registered SciPost users): | Bitan Roy |
| Submission information | |
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| Preprint Link: | scipost_202403_00040v1 (pdf) |
| Date submitted: | 2024-03-29 17:47 |
| Submitted by: | Roy, Bitan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Traditional topological materials belong to different Altland-Zirnbauer symmetry classes (AZSCs) depending on their non-spatial symmetries. Here we introduce the notion of hybrid symmetry class topological insulators (HSCTIs): A fusion of two different AZSC topological insulators (TIs) such that they occupy orthogonal Cartesian hyperplanes and their universal massive Dirac Hamiltonian mutually anticommute. The boundaries of HSCTIs can also harbor TIs, typically affiliated with an AZSC different from the parent ones. As such, a fusion between planar quantum spin Hall and vertical Su-Schrieffer-Heeger insulators gives birth to a three-dimensional HSCTI, accommodating quantum anomalous Hall insulators and quantized Hall conductivity on the top and bottom surfaces. Such a response is shown to be stable against weak disorder. We extend this construction to encompass crystalline HSCTI and topological superconductors, and beyond three dimensions. Possible (meta)material platforms to harness HSCTIs are discussed.
Current status:
Reports on this Submission
Report 1 by Jasper van Wezel on 2024-5-1 (Invited Report)
Strengths
1. well-written
2. topical
3. broadly applicable
Weaknesses
1. presentation / claims misleading in several points
2. detailed example but no general proof
Report
The authors introduce the concept of "hybrid symmetry class topological insulators" and work out one particular example in detail.
The manuscript is very well-written, and the analysis of the example is both clear and thorough.
Moreover, the idea of combining two types of topological insulators to create a third is certainly useful and seems versatile and broadly applicable in follow-up work.
The content is therefore suitable for SciPost Physics.
However, I believe the way this idea is presented in the current manuscript is misleading in several central aspects.
I would like to suggest that the authors phrase these differently.
In particular:
1) the authors claim several times that their results go beyond the Altland-Zirnbauer classification.
However, this is simply not true, and moreover, not possible within the current setup. The Hamiltonian of Eq. (3) is a 3D Hamiltonian for non-interacting spin-1/2 particles in a two-orbital lattice. As written by the authors themselves below Eq. (4), this Hamiltonian falls in class A of the Altland-Zirnbauer classification, which in 3D is always trivial. This agrees with the observation of the authors that introducing a single (infinitely large) boundary into the periodic system along any direction results in an absence of surface states. The Altland-Zirnbauer classification does not say anything about the boundaries of boudaries (see also point 2 below), so as far as I can see the model introduced by the authors neatly fits into the Altland-Zirnbauer paradigm.
2) The authors also claim that the model of Eq. (3) is not a higher-order toplogical insulator (HOTI). However, introducing a boundary of the boudary (that is, cutting the periodic system in two orthogonal directions) may result in the emergence of edge states along the hinges. This clearly shows, as also argued by the authors, that the 3D system is a trivial insulator, while its 2D surface Hamiltonian (in one direction) is a topological insulator. A trivial insulator whose edges are topological insulators is the textbook definition of a second order topological insulator. I therefore do not understand why the authors insist their model is not a HOTI.
3) The authors present their results in very general terms, suggesting that all results are generic and that their construction will work for any combination of topological systems. However, they analyse only a single model in detail and discuss broader applications only in terms of extensions of that one model. There is no proof that any of the presented results are applicable more generally. In fact, some results certainly are not. For example, the topological invariant of eq. (5) should in general be Z-valued, rather than Z2-valued (being an invariant for a QAHI), and already fails to apply to the system with C4 symmetry in section 4 (as mentioned by the authors).
I would suggest that the authors are open about these aspects: their work provides a methodology for constructing HOTIs from lower-dimensional topological systems, and they analyse one particular example in great detail. This is a worthwhile result, without the need to claim anything more.
I also noticed some minor details:
- In the introduction, band inversions at TRIM are mentioned in a sentence referring to all AZ classes. Since TRIM do not have any special meaning in TRS-broken classes, this statement should be revised.
- The terminology "hybrid" can be confusing: the authors refer to hybridization between two terms in the Hamiltonian, rather than hybridization between spatially separated systems with an interface. It would be good to make this explicit early on.
- In the first sentence of section 2, the author mention "the" model, where they probably mean "a" model.
- It would be good to include details of the KWANT algorithm in appendix C.
Requested changes
- Rephrase the presentation of the results to avoid misleading claims.
- Consider minor points mentioned in the report.
Recommendation
Ask for major revision