Bulk-edge correspondence for Chern topological phases: A viewpoint from a generalized index theorem

Abstract

We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear dispersion but also with higher order derivatives arising from generic band structures. Using a generalized index theorem valid for such systems, we show the equivalence between the spectral flow of the edge states and the Chern numbers specifying the bulk systems.

17 pages, final version

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• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Anomalous bulk-edge correspondence in continuous media
• Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors
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• The interacting Rice-Mele model: bulk and boundaries
• Discovery of Higher-Order Topological Insulators using the Spin Hall Conductivity as a Topology Signature
• Surface Green's functions and boundary modes using impurities: Weyl semimetals and topological insulators
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• Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators
• Surface charge theorem and topological constraints for edge states: An analytical study of one-dimensional nearest-neighbor tight-binding models
• Majorana bound states in a superconducting Rashba nanowire in the presence of antiferromagnetic order
• Characterization of edge states in perturbed honeycomb structures
• Dual Topological Insulator Device with Disorder Robustness
• Chiral Flow in One-dimensional Floquet Topological Insulators
• Topological chiral modes in random scattering networks
• Symmetry protected weak topological phases in a superlattice
• Spin Hall effect in AA-stacked bilayer graphene
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Topological Corner States in Graphene by Bulk and Edge Engineering
• Odd-Parity Spin-Triplet Superconductivity in Centrosymmetric Antiferromagnetic Metals
• Long-time relaxation dynamics of a spin coupled to a Chern insulator
• Defects in Graphene : A Topological Description
• Delocalization of edge states in topological phases
• Complete absorption of topologically protected waves
• Dirac Fermions and Topological Phases in Magnetic Topological Insulator Films
• Self-consistent study of topological superconductivity in two-dimensional quasicrystals
• Asymmetric transport for magnetic Dirac equations
• Topological Phases in Nodeless Tetragonal Superconductors
• Non-Hermitian $C_{NH}=2$ Chern insulator protected by generalized rotational symmetry
• Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints
• Index of Dirac operators and classification of topological insulators
• Quantum dot coupled to topological insulators: The role of edge states
• Intrinsic emergence of Majorana modes in Luttinger j=3/2 systems
• Topological in-gap chiral edge states in superconducting Haldane model with spin-orbit coupling
• Topology of Fermi Surfaces and anomaly inflows
• Exact lattice-model calculation of boundary modes for Weyl semimetals and graphene
• Identification of the Majorana edge modes in tight-binding systems based on the Krylov method
• Band rearrangement through the 3D-Dirac equation with boundary conditions, and the corresponding topological change
• Proof of bulk-edge correspondence for band topology by Toeplitz algebra