Multipole higher-order topology in a multimode lattice

Abstract

The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of various nature. Higher-order topological insulators further expand this plethora of possibilities towards extended range of structure dimensionalities. Here, we put forward a novel class of twodimensional multipolar higher-order topological insulators that arise due to the interference of the degenerate modes of the individual meta-atoms generalizing the mechanism of spin-orbit coupling in condensed matter. We prove that this model features disorder-robust corner modes and cannot be reduced to the known crystalline topological phases or conventional quadrupole insulators, providing the first example of multipolar topology in a C3-symmetric lattice. The multimode nature of the lattice enables flat bands and corner states with extreme localization and allows to tune the topology of the bands via on-site properties. We support our predictions by assembling the designed structure and observing multipolar topological corner states experimentally.

Disentangled Higher‐Orbital Bands and Chiral Symmetric Topology in Confined Mie Resonance Photonic Crystals

“…For instance, negative coupling can be realized in a photonic waveguide array with both s-and p-orbitals and that octupole insulators can be observed in d-wave photonic bands. [36][37][38][39] However, these few works on the higher-orbital bands in photonic systems are limited in waveguide arrays which have a longitudinal direction and therefore possess a relatively large volume size [36,40] and can hardly be extended to 3D lattices. More importantly, the higherorbital bands are always entangled and therefore toxic for applications.…”

Photonic Molecule Approach to Multiorbital Topology

“…We anticipate that our approach unlocks an entire plethora of topological phenomena including higher-order topological physics and flat bands at optical wavelengths with possible generalizations toward other platforms such as polaritonics or acoustics. Recently, several works have been proposed to harness multiorbital physics to tailor the topological properties of two-dimensional photonic systems such as the higher-order crystalline topology in naturally p x - p y -hybridized kagome lattices, , higher-order quadrupole topology in a bipartite square s - p -hybridized lattice, and other unconventional types of multipole topology, as well as spinful generalizations of known higher-order topological insulators. ,, …”

“…A recently suggested alternative is to optimize the responses of the individual meta-atoms achieving an accidental degeneracy of their modes. − Such degenerate modes play a role analogous to the orbital or spin degrees of freedom in condensed matter or cold atom optical lattices. − Since the number and the symmetry of the degenerate modes can be tailored on demand, this opens up a rich plethora of novel topological phases. While this appealing strategy can be implemented directly at microwave frequencies, its realization in the visible range is severely hindered due to the fabrication limitations.…”