Fabian R. Lux^1,2, Sumit Ghosh³, Pascal Prass¹, Emil Prodan² and Yuriy Mokrousov^1,3

¹Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany. ²Department of Physics, Yeshiva University, New York, NY 10016, USA. ³Peter Grunberg Institut and Institute for Advanced Simulation, Forschungszentrum Julich and JARA, 52425 Julich, Germany.

DOI: 10.48550/arXiv.2103.01047

This is a repository for code, related to our paper on the "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 electronic states 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 hypertorus, 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 non-smooth textures of spins and charges containing topological defects.

The repository is divided in three parts.

1. ./code contains the Python source code which sets up and diagonalizes the spin Hamiltonians
2. ./gfx/ contains the both the data analysis and the data sets which went into the creation of the figures in the manuscript
3. ./tex contains LaTeX source for the manuscript itself and its Supplemental Material