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Model non-Hermitian topological operators without skin effect: A general principle of construction
by Daniel J. Salib, Sanjib Kumar Das and Bitan Roy
Submission summary
| Authors (as registered SciPost users): | Bitan Roy |
| Submission information | |
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| Preprint Link: | scipost_202404_00018v2 (pdf) |
| Date submitted: | Oct. 15, 2025, 10:28 p.m. |
| Submitted by: | Bitan Roy |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We propose a general principle of constructing non-Hermitian (NH) operators for insulating and gapless topological phases in any dimension ($d$) that over an extended NH parameter regime feature real eigenvalues and zero-energy topological boundary modes, when in particular their Hermitian counterparts are also topological. However, the topological zero modes disappear when the NH operators simultaneously accommodate real and imaginary (in periodic systems) or display complex (in systems with open boundary conditions) eigenvalues. These systems are always devoid of NH skin effects, {\color{blue}as has also been confirmed from the scaling of the inverse participation ratio}, thereby extending the realm of the bulk-boundary correspondence to NH systems in terms of solely the left or right zero-energy boundary localized eigenmodes. We showcase these general and robust outcomes for NH topological insulators in $d=1,2$ and $3$, encompassing their higher-order incarnations, as well as for NH topological Dirac, Weyl, and nodal-loop semimetals. Possible realizations of proposed NH topological phases in designer materials, optical lattices, and classical metamaterials are highlighted.
List of changes
1. We now cite Phys. Rev. B 99, 081103(R) (2019) as Ref. 63.
2. We state the unitary equivalence between our chosen form of the SSH model and the original one available in the literature (Refs. 82-84).
3. We replace Fig. 2(a) such that the eigenspectrum is particle-hole symmetrical.
4. In “Discussion & outlook” section, we propose an extension of the current work to include NH topological models without the NH skin effect as a future direction.
Changes in the revised manuscript (shown in BLUE) in response to Referee 1:
1. We expand Appendix C on the discussion related to the topological invariants for the NH topological models devoid of NHSE that we introduced in this work.
2. We expand the discussion on the future research direction related to NH topological superconductors, devoid of NHSE and add new references as Refs. 98-104.
3. At the end of Appendix B, we state that future work will identify different broken spatial symmetries leading to different types of NHSE.
4. Second paragraph of Introduction: In the sentence starting with “Typically, NH operators display skin effect …” we clarify that this is the case for NH topological models.
5. Second paragraph of Introduction: We state that although NHSE-free model NH operators were studied in various other contexts, such as optics, photonics, and electronics and cite the papers the referee mentioned as Refs. 80 and 81, so far there was no such construction for topological phases, which motivates the current work.
6. Discussion & outlook section: We cite the work by Halder et. al. PRB 109, 115407 (2024) as Ref. 94 and compare their construction with ours.
7. We add a new section on the inverse participation ratio (IPR) as Sec. 4 and Fig. 6 to establish the absence of NHSE in our construction. We have also expanded the discussion from Appendix C with an analysis of the IPR to establish the presence of NHSE and existence of both extended and localized modes in the presence of NHSE. See Figs. 8 and 9.
8. We rewrite the flagged sentence from the caption of Fig. 4 appropriately.
9. We expand the caption of Fig. 5 to clarify its purpose.
10. We further expand the sentence ending with “as anticipated” in Sec. 3.1 to justify the use of this phrase.
11. We clarify the necessity of adding a small amount of disorder to ensure the bi-orthonormality condition while using the Python-based numerical packages for NH systems.
12. In Appendixes B and C, we define the Pauli matrices in terms of the Gamma matrices.
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