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A $C^\ast$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals
by Pascal Prass, Fabian R. Lux, Emil Prodan, Duco van Straten, Yuriy Mokrousov
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Fabian Lux · Pascal Prass |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2403.11912v3 (pdf) |
| Code repository: | https://github.com/prasspascal/chern_numbers_in_skyrmion_crystals |
| Date accepted: | 2024-10-29 |
| Date submitted: | 2024-10-15 15:03 |
| Submitted by: | Prass, Pascal |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Understanding the interaction of real- and reciprocal space topology in skyrmion crystals is an open problem. We approach it from the viewpoint of $C^\ast$-algebras and calculate all admissible Chern numbers of a strongly coupled tight-binding skyrmion system on a triangular lattice as a function of Fermi energy and texture parameters. Our analysis reveals the topological complexity of electronic states coupled to spin textures, and the failure of the adiabatic picture to account for it in terms of emergent electromagnetism. On the contrary, we explain the discontinuous jumps in the real-space winding number in terms of collective evolution in real-, reciprocal, and mixed space Chern numbers. Our work sets the stage for further research on topological dynamics in complex dynamic spin textures coupled to external fields.
Author comments upon resubmission
Please find attached a list of changes made to the manuscript. Our point-by-point response to the questions and comments raised by the referee has can be found in the report section of the submission page.
Sincerely, and on behalf of all co-authors,
Pascal Prass
List of changes
References:
1. DOI added to Ref. [63] (former [61])
2. Ref. [11] and [31] added
Figures:
1. Panels in former Fig. 3 arranged into Fig. 3 and Tbl. 1
Main text:
1. Added context to Eq. 5
2. Additional paragraph at the end of Sec. 2.1
3. Rewritten first paragraph of Sec. 2.2
4. Shortened last paragraph of Sec. 2.4
5. Added context to Fig. 1
6. Changed form of Eq. 74 and 75
7. Added context to Eq. 102
8. Fixed order of operators in Eq. 108
9. Added context to Fig. 3
10. Added context to Tab. 1
11. Added Ref. [11] and [31] with context
12. Small corrections of spelling and typing mistakes
Published as SciPost Phys. Core 7, 080 (2024)