Atiyah-Hirzebruch spectral sequence in band topology: General formalism and topological invariants for 230 space groups
Ken Shiozaki, Masatoshi Sato, Kiyonori Gomi
Abstract
We study the Atiyah-Hirzebruch spectral sequence (AHSS) for equivariant $K$ theory in the context of band theory. Various concepts in band theory, such as irreps at high-symmetry points, compatibility relations, topological gapless points, and singularities, fit naturally into the AHSS. As an application of the AHSS, we get the complete list of topological invariants for 230 space groups without time-reversal or particle-hole invariance. We find that many torsion topological invariants appear even for symmorphic space groups.
Topics & Concepts
Formalism (music)Topology (electrical circuits)Zero-dimensional spaceSpectral sequenceMathematicsPure mathematicsSpectral spacePhysicsTopological spaceTopological vector spaceCombinatoricsArtVisual artsCohomologyMusicalTopological Materials and PhenomenaQuantum Mechanics and Non-Hermitian PhysicsAlgebraic structures and combinatorial models