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Results tagged with topology
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user 185226
In mathematics, topology examines the properties of space (such as connectedness and compactness) that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing.
7
votes
Topological indices for systems that lack translational invariance
The Bott index is essentially limited to finite, 2D systems with periodic boundary conditions. There may be some applications of the Bott index to a 1D system that will be found someday. I assume yo …
- 450
0
votes
Is there a topological invariance/winding number for non-translation invariance system?
There are several index formulas you can use. In addition to papers by Emil Prodan, you should look at the book he wrote with Schulz-Baldes, "Bulk and Boundary Invariants for Complex Topological Insu …
- 450
6
votes
What is the topological space in “topological materials/phases of matter”?
The misunderstanding many have is that topology just the study of topological spaces. It is really also about continuous functions between two topological spaces. … Finally, many more modern calculations involve operator theory or operator algebras, so there is only noncommutative topology where there are not really any topological spaces at all. …
- 450
2
votes
Alternatives for calculating topological invariants in topological materials
This is too big a question to answer fully. Let me start by explaining why in a single symmetry class we need so many invariants.
Consider just Chern insulators, and ignore interactions. We want …
- 450