Bulk-interface correspondences for one dimensional topological materials with inversion symmetry

TL;DR

This paper establishes a rigorous bulk-interface correspondence for one-dimensional topological materials with inversion symmetry, linking topological invariants to interface modes in both continuum and lattice models.

Contribution

It provides a precise and rigorous formulation of the bulk-interface correspondence for 1D inversion-symmetric topological materials, including continuum and lattice models.

Findings

Proves the bulk-interface correspondence for continuum models using edge mode parity.

Establishes the role of the Zak phase and index theory for lattice models.

Applies results to dislocation models in 1D topological materials.

Abstract

The interface between two materials described by spectrally gapped Hamiltonians is expected to host an in-gap interface mode, whenever a certain topological invariant changes across the interface. We provide a precise statement of this bulk-interface correspondence, and its rigorous justification. The correspondence applies to continuum and lattice models of interfaces between one-dimensional materials with inversion symmetry, with dislocation models being of particular interest. For continuum models, the analysis of the parity of the "edge" Bloch modes is the key component in our argument, while for the lattice models, the relative Zak phase and index theory are.