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Title: Unified topological characterization of electronic states in spin textures from noncommutative K -theory
The nontrivial topology of spin systems such as skyrmions in real space can promote complex electronic states. Here, we provide a general viewpoint at the emergence of topological spectral gaps in spin systems based on the methods of noncommutative K -theory. By realizing that the structure of the observable algebra of spin textures is determined by the algebraic properties of the noncommutative torus, we arrive at a unified understanding of topological electronic states which we predict to arise in various noncollinear setups. The power of our approach lies in an ability to categorize emergent topological states algebraically without referring to smooth real- or reciprocal-space quantities. This opens a way towards an educated design of topological phases in aperiodic, disordered, or nonsmooth textures of spins and charges containing topological defects. Published by the American Physical Society2024  more » « less
Award ID(s):
1823800 2131760
PAR ID:
10555583
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
APS
Date Published:
Journal Name:
Physical Review Research
Volume:
6
Issue:
1
ISSN:
2643-1564
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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