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Abstract
Wave trapping and manipulation are at the heart of modern integrated photonics and acoustics. Grand challenges emerge on increasing the integration density and reducing the wave leakage/noises due to fabrication imperfections, especially for waveguides and cavities at subwavelength scales. The rising of robust wave dynamics based on topological mechanisms offers possible solutions. Ideally, in a three-dimensional (3D) topological integrated chip, there are coexisting robust two-dimensional (2D) interfaces, one-dimensional (1D) waveguides and zero-dimensional (0D) cavities. Here, we report the experimental discovery of such a dimensional hierarchy of the topologically-protected 2D surface states, 1D hinge states and 0D corner states in a single 3D system. Such an unprecedented phenomenon is triggered by the higher-order topology in simple-cubic sonic crystals and protected by the space group \[{P}_{m\bar{3}m}\]. Our study opens up a new regime for multidimensional wave trapping and manipulation at subwavelength scales, which may inspire future technology for integrated acoustics and photonics.
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Details

1 National Laboratory of Solid State Microstructures, Department of Materials Science and Engineering, Nanjing University, Nanjing, China
2 National Laboratory of Solid State Microstructures, Department of Materials Science and Engineering, Nanjing University, Nanjing, China; Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing, China
3 School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou, China
4 National Laboratory of Solid State Microstructures, Department of Materials Science and Engineering, Nanjing University, Nanjing, China; Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing, China; Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
5 National Laboratory of Solid State Microstructures, Department of Materials Science and Engineering, Nanjing University, Nanjing, China; Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China