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Topological states between inversion symmetric atomic insulators
by Ana Silva and Jasper van Wezel
This Submission thread is now published as
|As Contributors:||Jasper van Wezel|
|Date submitted:||2021-05-03 10:24|
|Submitted by:||van Wezel, Jasper|
|Submitted to:||SciPost Physics|
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary correspondence has been well-tested for strong topological invariants, and forms the basis for all proposed technological applications of topology. Here, we report that a group of weak topological invariants, which depend only on the symmetries of the atomic lattice, also induces a particular type of bulk-boundary correspondence. It predicts the presence or absence of states localised at the interface between two inversion-symmetric band insulators with trivial values for their strong invariants, based on the space group representation of the bands on either side of the junction. We show that this corresponds with symmetry-based classifications of topological materials. The interface modes are protected by the combination of band topology and symmetry of the interface, and may be used for topological transport and signal manipulation in heterojunction-based devices.
Published as SciPost Phys. 10, 137 (2021)
Author comments upon resubmission
We would like to thank the referees for their time and effort in reviewing our submission, and for their many positive comments regarding our work. In particular, the referees note that the paper is “very well written", presents "strong" or "general, model-independent" results, and is likely to "lead to multiple follow-up theoretical and experimental investigations".
Both referees raised similar concerns, which we believe are primarily based in our failure to give a sufficiently clear definition of our use of the terms "strong topology" and "topological protection" in the original manuscript. Additionally, both referees ask for an explicit example of our proposed interface states.
In the attached, revised manuscript we address both concerns of the referees in detail. We extended the introduction, and now explicitly define the meaning of all terms that are open to multiple interpretations. We also introduce an extensive new section with three additional figures, describing two explicit examples in which the proposed topological interface states arise. We show their existence in numerical simulations, and probe their robustness in the way suggested by the referees.
We believe these changes adequately address the concerns raised by the referees, and respectfully ask you to reconsider the attached manuscript. Below, we respond to the comments of both referees point by point.
Ana Silva and Jasper van Wezel.
List of changes
Our reply letter includes a figure, which we cannot upload here -- For our replies to the comments made by referees, and an explanation of the changes made, please see our "response to the referee comments" (submitted earlier to the SciPost page for this submission).
Submission & Refereeing History
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- Report 2 submitted on 2021-01-27 14:00 by Anonymous
- Report 1 submitted on 2021-01-22 14:21 by Anonymous
Reports on this Submission
Anonymous Report 1 on 2021-5-15 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202101_00003v2, delivered 2021-05-15, doi: 10.21468/SciPost.Report.2919
The authors have included new examples which nicely illustrate the properties of the interface states.
In my previous report I pointed out that it seems likely that it is possible to introduce a perturbation which obeys the symmetries but moves the interface states in energy to the conduction or valence band on either side of the interface. Thus, the interface states hybridise with the bulk states and are no longer localised at the interface.
In the examples considered by the authors, they indeed found that the interface states can be moved arbitrary close to the gap edge. The authors claim that the topological interface states “enjoy some form of topological protection in the sense that they must exist in the gap and cannot be destroyed or brought into the bulk”. However, one could alternatively argue that since their energy can be brought arbitrarily close to the gap edge also the localization length can diverge, and therefore it is impossible to distinguish them from the bulk states in practice. In my opinion, this is still not discussed clearly enough in the manuscript. The authors call this result counterintuitive and therefore they do not discuss this in the manuscript. I think that this information should be available for the readers of the manuscript. It is therefore necessary to include in the manuscript the figure which the authors have already included in the response letter, and to write it clearly that the interface states can be brought arbitrarily close to the gap edge so that their localization length can diverge.