Solitons in higher-order topological insulator created by unit cell twisting

TL;DR

This paper demonstrates that twisting waveguides within each unit cell of a square lattice can induce higher-order topological insulators with coexisting corner modes, expanding the design possibilities for topological photonic systems.

Contribution

It introduces a novel method of creating higher-order topological insulators through unit cell twisting without changing intracell distances, revealing new topological phases and coexisting corner modes.

Findings

Twisting waveguides induces topological gaps supporting corner modes.

Supports two coexisting types of corner modes in different spectral gaps.

Both types of corner solitons can be stable simultaneously.

Abstract

We show that higher-order topological insulators can be created from usual square structure by twisting waveguides in each unit cell around the axis passing through the center of the unit cell, even without changing intracell distance between waveguides. When applied to usual square array, this approach produces two-dimensional generalization of Su-Schrieffer-Heeger (SSH) structure supporting topological corner modes with propagation constants belonging to two forbidden spectral gaps opening only for twist angles from certain interval. In contrast to usual SSH arrays, where higher-order topology is typically introduced by diagonal waveguide shifts and only one type of corner states exists, our SSH-like structure in topological phase supports two co-existing types of in-phase and out-of-phase corner modes appearing in two different topological gaps that open in the spectrum. Therefore, twisting of the unit cell qualitatively changes topological properties of the system, offering a new degree of freedom in creation of higher-order topological phases. In material with focusing cubic nonlinearity two coexisting types of topological corner solitons emerge from these modes, whose existence and stability properties are studied here. Despite different internal structure, both such modes can be simultaneously dynamically stable in the appreciable part of the topological gap.