Cobordism invariance of topological edge-following states
Matthias Ludewig, Guo Chuan Thiang
Abstract
We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore, the gap-filling spectra contribute to quantised current channels, which follow and are localised at the possibly complicated boundary. This index obstruction is shown to be insensitive to deformations of the domain boundary, so the phenomenon is generic for magnetic Laplacians modelling quantum Hall systems and Chern topological insulators. A key construction is a quasi-equivariant version of Roe's algebra of locally compact finite propagation operators.
Topics & Concepts
CobordismMathematicsEquivariant mapBoundary (topology)Hamiltonian (control theory)Boundary value problemPure mathematicsPhysicsTopology (electrical circuits)Mathematical analysisCombinatoricsMathematical optimizationTopological Materials and PhenomenaQuantum and electron transport phenomenaQuantum many-body systems