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The bulk band topology of symmetry invariant adiabatic systems in the thermodynamic limit are considered to be determined by the hopping energy. In this work, we present that in closed classical systems, due to generalized chiral symmetry broken, the on-site energy cannot always be regarded as identical and can crucially impact the topological properties of the systems. Based on a finite one-dimensional chain, we demonstrate that the non-equivalent on-site energy of bulk lattices affects the topological phases of the bands, and the on-site energy of end lattices affects the existence of the topological states. Along these lines, the correspondence with generalized chiral symmetry in acoustic system is rigorously proposed. Our work provides a new degree of freedom for topological classical systems, and can be generalized to higher-dimensions and non-Hermitian conditions.
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The Dzyaloshinskii-Moriya interaction (DMI) in magnetic systems stabilizes spin textures with preferred chirality, applicable to next-generation memory and computing architectures. In perpendicularly magnetized heavy-metal/ferromagnet films, the interfacial DMI originating from structural inversion asymmetry and strong spin-orbit coupling favors chiral Neel-type domain walls (DWs) whose energetics and mobility remain at issue. Here, we characterize a new effect in which domains expand unidirectionally in response to a combination of out-of-plane and in-plane magnetic fields, with the growth direction controlled by the in-plane field strength. These growth directionalities and symmetries with applied fields cannot be understood from static treatments alone. We theoretically demonstrate that perpendicular field torques stabilize steady-state magnetization profiles highly asymmetric in elastic energy, resulting in a dynamic symmetry breaking consistent with the experimental findings. This phenomenon sheds light on the mechanisms governing the dynamics of Neel-type DWs and expands the utility of field-driven DW motion to probe and control chiral DWs.
Recent work predicted the existence of isotropic chiral phonon dispersion relations of the lowest bands connected to isotropic acoustical activity in cubic crystalline approximants of 3D chiral icosahedral metamaterial quasicrystals. While these architectures are fairly broadband and presumably robust against fabrication tolerances due to orientation averaging, they are extremely complex, very hard to manufacture experimentally, and they show effects which are about an order of magnitude smaller compared to those of ordinary highly anisotropic chiral cubic metamaterial crystals. Here, we propose and analyze a chiral triclinic metamaterial crystal exhibiting broadband isotropic acoustical activity. These 3D truss lattices are much less complex and exhibit substantially larger effects than the 3D quasicrystals at the price of being somewhat more susceptible to fabrication tolerances. This susceptibility originates from the fact that we have tailored the lowest two transverse phonon bands to exhibit an accidental degeneracy in momentum space.
We introduce $mathbb Z_2$-valued bulk invariants for symmetry-protected topological phases in $2+1$ dimensional driven quantum systems. These invariants adapt the $W_3$-invariant, expressed as a sum over degeneracy points of the propagator, to the respective symmetry class of the Floquet-Bloch Hamiltonian. The bulk-boundary correspondence that holds for each invariant relates a non-zero value of the bulk invariant to the existence of symmetry-protected topological boundary states. To demonstrate this correspondence we apply our invariants to a chiral Harper, time-reversal Kane-Mele, and particle-hole symmetric graphene model with periodic driving, where they successfully predict the appearance of boundary states that exist despite the trivial topological character of the Floquet bands. Especially for particle-hole symmetry, combination of the $W_3$ and the $mathbb Z_2$-invariants allows us to distinguish between weak and strong topological phases.
Topological states nurtures the emergence of devices with unprecedented functions in photonics, plasmonics, acoustics and phononics. As one of the recently discovered members, higher-order topological insulators (HOTIs) have been increasingly explored, featuring lower-dimensional topological boundary states, leading to rich mechanisms for topological manipulation, guiding and trapping of classical waves. Here, we provide an overview of current developments of HOTIs in classical waves including basic principles, unique physical properties, various experimental realizations, novel phenomena and potential applications. Based on these discussions, we remark on the trends and challenges in this field and the impacts of higher-order topology on other research fields.
Topological photonic systems represent a new class of optical materials supporting boundary modes with unique properties, not found in conventional photonics. While the early research on topological photonics has focused on edge and surface modes in 2D and 3D systems, respectively, recently higher-order topological insulators (HOTIs) supporting lower-dimensional boundary states have been introduced. In this work we design and experimentally realize a photonic kagome metasurface exhibiting a Wannier-type higher-order topological phase. We demonstrate and visualize the emergence of a topological transition and opening of a Dirac cone by directly exciting the bulk modes of the HOTI metasurface via solid-state immersion spectroscopy. The open nature of the metasurface is then utilized to directly image topological boundary states. We show that, while the domain walls host 1D edge states, their bending induces 0D higher-order topological modes confined to the corners. The demonstrated metasurface hosting topological boundary modes of different dimensionality paves the way to a new generation of universal and resilient optical devices which can controllably scatter, trap and guide optical fields in a robust way.
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