Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems

TL;DR

This paper develops a topological framework to identify and understand anyonic excitations in fractional quantum anomalous Hall systems, crucial for their use in topological quantum computing.

Contribution

It introduces a novel algebro-topological approach linking band topology to anyon properties via equivariant cohomotopy, advancing the theoretical understanding of FQAH systems.

Findings

Admissible braiding phases are 2C-th roots of unity.

Provides a topological criterion for identifying anyons in FQAH.

Lays groundwork for symmetry-protected topological order analysis.

Abstract

Recently observed fractional quantum anomalous Hall materials (FQAH) are candidates for topological quantum hardware, but their required anyon states are elusive. We point out dependence on monodromy in the fragile band topology in 2-cohomotopy. An algebro-topological theorem of Larmore & Thomas (1980) then identifies FQAH anyons over momentum space. Admissible braiding phases are 2C-th roots of unity, for C the Chern number. This lays the foundation for understanding symmetry-protected topological order in FQAH systems, reducing the problem to computations in equivariant cohomotopy.