Observation of nonlinear higher-order topological insulators with unconventional boundary truncations

TL;DR

This paper introduces a novel method for constructing higher-order topological insulators using incomplete unit cells, leading to new boundary modes and stable nonlinear solitons, broadening the understanding of HOTIs.

Contribution

The authors propose and experimentally demonstrate a new approach to HOTIs utilizing incomplete unit cells, enabling boundary modes regardless of Wannier center positions and revealing stable topological solitons.

Findings

Boundary modes emerge in systems with incomplete unit cells for both trivial and nontrivial Wannier centers.

Stable topological solitons bifurcate from boundary states in nonlinear waveguide arrays.

The approach broadens the class of HOTIs and enables observation of boundary states with various symmetries.

Abstract

In higher-order topological insulators (HOTIs), topologically nontrivial phases are usually associated with the shift of Wannier centers to topologically nontrivial positions on the edges of the unit cells, and the emergence of fractional spectral charges in the corners of the lattice upon its truncation that keeps the number of its unit cells integer. Here we propose theoretically and illustrate experimentally a different approach to the construction of HOTIs. This approach utilizes lattices with incomplete unit cells and achieves localized modes of topological origin across a broader parameter space. When truncation disrupts translational symmetry by cutting through the interior of multiple unit cells, boundary modes in our system emerge for both trivial and topologically nontrivial positions of the Wannier centers. We link these modes to the appearance of fractional Wannier centers. We also demonstrate that linear boundary states give rise to rich families of stable solitons bifurcating from them in the presence of focusing nonlinearity. Multiple types of thresholdless topological solitons with different internal symmetries are observed in waveguide arrays with triangular configurations featuring incomplete unit cells for any dimerization of waveguide spacings. Our results expand the family of HOTIs and pave the way for the observation of boundary states with different symmetries.