An article that we are writing at CQTS:
Classifying Fragile Crystalline Fractional Chern Phases
by Equivariant 2-Cohomotopy
main: [pdf draft to appear here]
supp: pdf (equivariant cell structures on 2-tori)
Abstract: We classify the crystalline fragile topological phases (as well as the possible topological orders) of 2-dimensional 2-band (fractional) Chern insulators. Despite the prominence and relevance of crystalline (fractional) Chern phases, such computations appear not to have previously been recorded or even considered. Mathematically, what we compute is equivariant 2-Cohomotopy of the Brillouin torus: The connected components (and their fundamental groups) of spaces of equivariant maps from the torus of crystal momenta to the 2-sphere of normalized 2-band gapped Bloch Hamiltonians: an unstable and generally abelian refinement of the popular but coarser K-theory classification. To make the account self-contained, we highlight the homotopy theoretic tools invoked in the computations, which may not have previously received attention in the topological phases community.
Following:
Last revised on July 23, 2025 at 09:15:34. See the history of this page for a list of all contributions to it.