Elastic Higher-Order Topological Insulator with Topologically Protected Corner States.

Topologically gapless edge states, characterized by topological invariants and Berry's phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons, and phonons. Recently, a new family of topological phases, dictated by the bulk polarization, has been observed, leading to the discovery of the higher-order topological insulators (HOTIs). So far, the HOTIs have been demonstrated in mechanical and electromagnetic systems and electrical circuits with quantized quadrupole polarization and, more recently, have been experimentally realized in optical and acoustic systems. Here, we realize the higher-order topological states in a two-dimensional (2D) continuous elastic system. We experimentally observe the gapped one-dimensional (1D) edge states, the trivially gapped zero-dimensional (0D) corner states, and the topologically protected 0D corner states. Compared with the trivial corner modes, the topological ones, immunizing against defects, are robustly localized at the obtuse-angled but not the acute-angled corners. The topological shape-dependent corner states open a new route for the design of the topologically protected and reconfigurable 0D localized resonances and provide an excellent platform for the topological transformation of the elastic energy among 2D bulk, 1D edge, and 0D corner modes.

The brain-inspired decoder for natural visual image reconstruction.

The visual system provides a valuable model for studying the working mechanisms of sensory processing and high-level consciousness. A significant challenge in this field is the reconstruction of images from decoded neural activity, which could not only test the accuracy of our understanding of the visual system but also provide a practical tool for solving real-world problems. Although recent advances in deep learning have improved the decoding of neural spike trains, little attention has been paid to the underlying mechanisms of the visual system. To address this issue, we propose a deep learning neural network architecture that incorporates the biological properties of the visual system, such as receptive fields, to reconstruct visual images from spike trains. Our model outperforms current models and has been evaluated on different datasets from both retinal ganglion cells (RGCs) and the primary visual cortex (V1) neural spikes. Our model demonstrated the great potential of brain-inspired algorithms to solve a challenge that our brain solves.

Observation of fractal higher-order topological states in acoustic metamaterials.

Topological phases of matter have been extensively investigated in solid-state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain almost unexplored. Fractals, being self-similar on different scales, are one of the intriguing complex geometries with non-integer dimensions. Here, we demonstrate fractal higher-order topological states with unprecedented emergent phenomena in a Sierpinski acoustic metamaterial. We uncover abundant topological edge and corner states in the acoustic metamaterial due to the fractal geometry. Interestingly, the numbers of the edge and corner states depend exponentially on the system size, and the leading exponent is the Hausdorff fractal dimension of the Sierpinski carpet. Furthermore, the results reveal the unconventional spectrum and rich wave patterns of the corner states with consistent simulations and experiments. This study thus unveils unconventional topological states in fractal geometry and may inspire future studies of topological phenomena in non-Euclidean geometries.