Cobordism invariance of topological edge-following states

DOI10.4310/ATMP.2022.V26.N3.A4arXiv2001.08339MaRDI QIDQ6333347

Publication date: 22 January 2020

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.

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Schrödinger operator, Schrödinger equation (35J10) Statistical mechanics of semiconductors (82D37) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Many-body theory; quantum Hall effect (81V70) Extension and compression of mappings in algebraic topology (55S36) Quantum channels, fidelity (81P47)

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