nLab unstable classification of topological phases -- references

Unstable classification of topological phases

Unstable classification of topological phases

Arguments that some effects in topological phases of matter are “unstable” or “fragile” in that the relevant deformation class of their valence bundles over the Brillouin torus is not their class in topological K-theory (as assumed by the K-theory classification of topological phases of matter) but an unstable homotopy class (what may be called a class in generalized nonabelian cohomology) such as of maps to a Grassmannian space (or more general flag variety) classifying (systems of) sub-bundles of a trivial vector bundle of fixed finite rank:

Influential precursor discussion:

More explicit highlighting of the role of the unstable case (and coinage of the term “fragile” for “unstable”):

Applications:

Expositions with an eye towards non-abelian braiding of band nodes in momentum space:

Last revised on June 3, 2025 at 17:38:45. See the history of this page for a list of all contributions to it.