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Real-space approach for the Euler class and fragile topology in quasicrystals and amorphous lattices
by Dexin Li, Citian Wang, Huaqing Huang
Submission summary
| Authors (as registered SciPost users): | Huaqing Huang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202405_00006v3 (pdf) |
| Date submitted: | 2024-08-19 10:19 |
| Submitted by: | Huang, Huaqing |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We propose a real-space formalism of the topological Euler class, which characterizes the fragile topology of two-dimensional systems with real wave functions. This real-space description is characterized by local Euler markers whose macroscopic average coincides with the Euler number, and it applies equally well to periodic and open boundary conditions for both crystals and noncrystalline systems. We validate this by diagnosing topological phase transitions in clean and disordered crystalline systems with the reality endowed by the space-time inversion symmetry $\mathcal{I}_{ST}$. Furthermore, we demonstrated the topological Euler phases in quasicrystals and even in amorphous lattices lacking any spatial symmetries. Our work not only provides a local characterization of the fragile topology but also significantly extends its territory beyond $\mathcal{I}_{ST}$-symmetric crystalline materials.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
Thank you for handling our manuscript, and we also would like to express our sincere gratitude to the referees for their careful review of our manuscript and their constructive comments. We have responded to the comments by the referee, and accordingly revised the manuscript. We hope that the revised manuscript can now be accepted for publication in SciPost Physics.
Sincerely,
Huaqing Huang
/On behalf of all Authors/
List of changes
According to the referees’ suggestions, we have made the following revisions:
1. add a paragraph in the revised manuscript that acknowledges the limitations and outlines potential future directions for research.