Photonic p-orbital higher-order topological insulators

TL;DR

This paper demonstrates the realization of p-orbital corner states in a photonic higher-order topological insulator, revealing their topological properties, symmetry protections, and nonlinear dynamics, thus advancing orbital physics in topological materials.

Contribution

It introduces the first experimental realization of p-orbital states in a photonic HOTI, highlighting the role of orbital-hopping symmetry and generalized winding number in topological protection.

Findings

P-orbital corner states are observed in a photonic Kagome HOTI.

Topological protection requires orbital-hopping symmetry and generalized chiral symmetry.

Nonlinearity induces dynamical rotation of the p-orbital states.

Abstract

The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter including orbital superfluidity and topological semimetals. Despite tremendous efforts in engineering synthetic cold-atom, electronic and photonic lattices to explore orbital physics, thus far high orbitals in an important class of materials, namely, the higher-order topological insulators (HOTIs), have not been realized. Here, we demonstrate p-orbital corner states in a photonic HOTI, unveiling their underlying topological invariant, symmetry protection, and nonlinearity-induced dynamical rotation. In a Kagome-type HOTI, we find that topological protection of the p-orbital corner states demands an orbital-hopping symmetry, in addition to the generalized chiral symmetry. Due to orbital hybridization, the nontrivial topology of the p-orbital HOTI is hidden if bulk polarization is used as the topological invariant, but well manifested by the generalized winding number. Our work opens a pathway for the exploration of intriguing orbital phenomena mediated by higher band topology applicable to a broad spectrum of systems.