Topological defects in a double-mirror quadrupole insulator displace diverging charge

TL;DR

This paper demonstrates that topological defects in quadrupole insulators do not carry quantized fractional charges, instead exhibiting diverging charge due to sublattice symmetry, challenging previous assumptions based on Wannier representations.

Contribution

It reveals that topological defects in quadrupole insulators do not host quantized charges and identifies sublattice symmetry as the key factor, contrasting prior beliefs based on higher order topology.

Findings

Local charge density decays as 1/r^2 with distance

Defect charge diverges, not quantized

Sublattice symmetry, not higher order topology, causes charge quantization

Abstract

We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier representation of a parametric defect and a disclination. Against the expectations, we find that the local charge density decays as $\sim 1/r^2$ with distance, leading to a diverging defect charge. We identify sublattice symmetry and not higher order topology as the origin of the previously reported charge quantization.