Cobordism invariance of topological edge-following states

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.

38 pages, 6 figures, revised for publication in ATMP

References in corpus (4)

• Higher-dimensional generalizations of the Berry curvature
• Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry
• Edge-following topological states
• The Geometry of (non-Abelian) Landau levels

Cited by in corpus (7)

• Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry
• Edge-following topological states
• Delocalized spectra of Landau operators on helical surfaces
• Locally equivalent quasifree states and index theory
• Topological edge states of 1D chains and index theory
• Interfaces of discrete systems - spectral and index properties
• Coarse geometric approach to topological phases: Invariants from real-space representations