Tailoring higher-order topological phases via orbital hybridization

TL;DR

This paper demonstrates a novel higher-order topological insulator phase in photonic waveguides, achieved through orbital hybridization, which enables control over topological properties using symmetry and degeneracy.

Contribution

It introduces an unconventional HOTI phase with unique polarization properties, realized via orbital mode degeneracy and hybridization in a square lattice photonic system.

Findings

Identified a HOTI phase with zero dipole and quadrupole polarization.

Linked topological properties to orbital degeneracy and hybridization.

Mapped the system to two rotated Su-Schrieffer-Heeger models.

Abstract

Higher-order topological insulators (HOTIs) have attracted much attention in photonics due to the tightly localized disorder-robust corner and hinge states. Here, we reveal an unconventional HOTI phase with vanishing dipole and quadrupole polarizations. This phase arises in the array of evanescently coupled waveguides hosting degenerate $s$- and $d$-type orbital modes arranged in a square lattice with four waveguides in the unit cell. As we prove, the degeneracy of the modes with the different symmetry gives rise to the nontrivial topological properties rendering the system equivalent to the two copies of anisotropic two-dimensional Su-Schrieffer-Heeger model rotated by 90$^\circ$ with respect to each other and based on $s\pm d$ hybridized orbitals. Our results introduce a route to tailor higher-order band topology leveraging both crystalline symmetries and accidental degeneracies of the different orbital modes.