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Cobordism invariance of topological edge-following states

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arxiv 2001.08339 v2 pith:IQJHRLCE submitted 2020-01-23 math-ph cond-mat.mes-hallmath.KTmath.MPmath.OA

classification math-phcond-mat.mes-hallmath.KTmath.MPmath.OA
keywords boundarydomaingap-fillingindexobstructionphenomenontopologicalalgebra
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Bulk-Edge Correspondence for Finite Two-dimensional Ergodic Disordered Systems

    math-ph 2025-12 conditional novelty 7.0 of 10

    For finite 2D ergodic disordered Hamiltonians, an angular-momentum edge index converges almost surely to a refined topological bulk index as the sample size goes to infinity.

  2. Generalized bulk-interface correspondence for non-quantized spin transport

    math-ph 2025-05 conditional novelty 7.0 of 10

    For tight-binding electron systems with nonconserved spin, the difference of bulk spin conductances across an interface equals the interface spin-drift conductance plus the interface spin-torque conductance.

  3. Bulk-edge correspondence in finite photonic structure

    math-ph 2025-01 conditional novelty 6.0 of 10

    For finite 2D photonic structures, the per-area edge circulation index converges to the bulk gap Chern number as the domain grows, conditional on unproved Green function bounds.

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