Dislocation charges reveal two-dimensional topological crystalline invariants

TL;DR

This paper establishes a direct link between dislocation charges and topological invariants in 2D crystalline insulators, enabling dislocation charges to serve as probes of crystalline topological phases.

Contribution

It introduces a one-to-one correspondence between dislocation charges and Berry phases, connecting them to topological invariants in symmetry-protected insulators.

Findings

Dislocation charges correspond to Berry phases in 2D insulators.

Dislocation charges reveal topological invariants protected by inversion and rotation symmetries.

Dislocation charges can be used as universal probes of crystalline topologies.

Abstract

We identify a one-to-one correspondence between the charge localized around a dislocation characterized by a generic Burgers vector and the Berry phase associated with the electronic Bloch waves of two-dimensional crystalline insulators. Using this correspondence, we reveal a link between dislocation charges and the topological invariants of inversion and rotation symmetry-protected insulating phases both in the absence and in the presence of time-reversal symmetry. Our findings demonstrate that dislocation charges can be used as generic probes of crystalline topologies.