Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
arXiv (Cornell University)(2023)
摘要
The topological classification of gapped band structures depends on the
particular definition of topological equivalence. For translation-invariant
systems, stable equivalence is defined by a lack of restrictions on the numbers
of occupied and unoccupied bands, while imposing restrictions on one or both
leads to “fragile” and “delicate” topology, respectively. In this article,
we describe a homotopic classification of band structures – which captures the
topology beyond the stable equivalence – in the presence of additional lattice
symmetries. As examples, we present complete homotopic classifications for
spinless band structures with twofold rotation, fourfold rotation and fourfold
dihedral symmetries, both in presence and absence of time-reversal symmetry.
Whereas the rules of delicate and fragile topology do not admit a bulk-boundary
correspondence, we identify a version of stable topology, which restricts the
representations of bands, but not their numbers, which does allow for anomalous
states at symmetry-preserving boundaries, which are associated with nontrivial
bulk topology.
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关键词
band structures,homotopic classification,topology,representation-protected
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