Dislocation as a bulk probe of higher-order topological insulators

TL;DR

This paper shows that dislocations in higher-order topological insulators can serve as bulk probes by hosting symmetry-protected in-gap modes at defect cores, revealing extended bulk-boundary correspondence.

Contribution

It introduces a theoretical framework demonstrating how dislocations can reveal higher-order topological states via localized in-gap modes.

Findings

Dislocations host symmetry-protected in-gap modes in HOT insulators.

The in-gap modes depend on the Burgers vector orientation.

Modes become gapless when the Burgers vector points toward lower-dimensional boundaries.

Abstract

Topological materials occupy the central stage in the modern condensed matter physics because of their robust metallic edge or surface states protected by the topological invariant, characterizing the electronic band structure in the bulk. Higher-order topological (HOT) states extend this usual bulk-boundary correspondence, so they host the modes localized at lower-dimensional boundaries, such as corners and hinges. Here we theoretically demonstrate that dislocations, ubiquitous defects in crystalline materials, can probe higher-order topology, recently realized in various platforms. We uncover that HOT insulators respond to dislocations through symmetry protected finite-energy in-gap electronic modes, localized at the defect core, which originate from an interplay between the orientation of the HOT mass domain wall and the Burgers vector of the dislocation. As such, these modes become gapless only when the Burgers vector points toward lower-dimensional gapless boundaries. Our findings are consequential for the systematic probing of the extended bulk-boundary correspondence in a broad range of HOT crystals, and photonic and phononic or mechanical metamaterials through the bulk topological lattice defects.