Square-root topological state of coupled plasmonic nanoparticles in a decorated Su-Schrieffer-Heeger lattice

Square-root higher-order topological insulators in a photonic decorated SSH lattice

Recently, there has been a surge of interest in square-root higher-order topological insulators (HOTIs) due to their unique topological properties inherited from their squared Hamiltonian. Different from conventional HOTIs, square-root HOTIs support paired corner states that exist in different bandgaps. In this work, we experimentally establish a series of two-dimensional photonic decorated Su-Schrieffer-Heeger (SSH) lattices by using the femtosecond-laser writing technique and thereby directly observe paired topological corner states. Interestingly, the higher-order topological properties of such square-root HOTIs are inherited from the parent Hamiltonian, which contains the celebrated 2D SSH lattice. The dynamic evolution of square-root corner states indicates that they exist in different bandgaps. This work not only provides a new platform to study higher-order topology in optics, it also brings about new possibilities for future studies of other novel HOTIs.

Topological edge states in photonic decorated trimer lattices

In recent years, topological insulators have been extensively studied in one-dimensional periodic systems, such as Su-Schrieffer-Heeger and trimer lattices. The remarkable feature of these one-dimensional models is that they support topological edge states, which are protected by lattice symmetry. To further study the role of lattice symmetry in one-dimensional topological insulators, here we design a modified version of the conventional trimer lattices, i.e., decorated trimer lattices. Using the femtosecond laser writing technique, we experimentally establish a series of one-dimensional photonic decorated trimer lattices with and without inversion symmetry, thereby directly observing three kinds of topological edge state. Interestingly, we demonstrate that the additional vertical intracell coupling strength in our model can change the energy band spectrum, thereby generating unconventional topological edge states with a longer localization length in another boundary. This work offers novel insight into topological insulators in one-dimensional photonic lattices.

Square-root higher-order Weyl semimetals

The mathematical foundation of quantum mechanics is built on linear algebra, while the application of nonlinear operators can lead to outstanding discoveries under some circumstances, such as the prediction of positron, a direct outcome of the Dirac equation which stems from the square-root of the Klein-Gordon equation. In this article, we propose a model of square-root higher-order Weyl semimetal (SHOWS) by inheriting features from its parent Hamiltonians. It is found that the SHOWS hosts both “Fermi-arc” surface and hinge states that respectively connect the projection of the Weyl points on the side surface and arris. We theoretically construct and experimentally observe the exotic SHOWS state in three-dimensional (3D) stacked electric circuits with honeycomb-kagome hybridizations and double-helix interlayer couplings. Our results open the door for realizing the square-root topology in 3D solid-state platforms.

The topological properties of square-root Weyl semimetals are derived from the square of the Hamiltonian. Here, the authors propose a tight-binding model for a square-root higher-order Weyl semimetal hosting both Fermi-arc surface and hinge states.