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Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator

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 Added by Haoran Xue
 Publication date 2021
  fields Physics
and research's language is English




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The interplay between real-space topological lattice defects and the reciprocal-space topology of energy bands can give rise to novel phenomena, such as one-dimensional topological modes bound to screw dislocations in three-dimensional topological insulators. We obtain direct experimental observations of dislocation-induced helical modes in an acoustic analog of a weak three-dimensional topological insulator. The spatial distribution of the helical modes is found through spin-resolved field mapping, and verified numerically by tight-binding and finite-element calculations. These one-dimensional helical channels can serve as robust waveguides in three-dimensional media. Our experiment paves the way to studying novel physical modes and functionalities enabled by topological lattice defects in three-dimensional classical topological materials.



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Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects. This is known as bulk-dislocation correspondence, in contrast to the conventional bulk-boundary correspondence featuring topological states at boundaries. However, to date rare compelling experimental evidences are presented for this intriguing topological observable, owing to the presence of various challenges in solid-state systems. Here, using a three-dimensional acoustic topological insulator with precisely controllable dislocations, we report an unambiguous experimental evidence for the long-desired bulk-dislocation correspondence, through directly measuring the gapless dispersion of the one-dimensional topological dislocation modes. Remarkably, as revealed in our further experiments, the pseudospin-locked dislocation modes can be unidirectionally guided in an arbitrarily-shaped dislocation path. The peculiar topological dislocation transport, expected in a variety of classical wave systems, can provide unprecedented controllability over wave propagations.
Topological phononic crystals (PCs) are periodic artificial structures which can support nontrivial acoustic topological bands, and their topological properties are linked to the existence of topological edge modes. Most previous studies focused on the topological edge modes in Bragg gaps which are induced by lattice scatterings. While local resonant gaps would be of great use in subwavelength control of acoustic waves, whether it is possible to achieve topological interface states in local resonant gaps is a question. In this article, we study the topological bands near local resonant gaps in a time-reversal symmetric acoustic systems and elaborate the evolution of band structure using a spring-mass model. Our acoustic structure can produce three band gaps in subwavelength region: one originates from local resonance of unit cell and the other two stem from band folding. It is found that the topological interface states can only exist in the band folding induced band gaps but never appear in the local resonant band gap. The numerical simulation perfectly agrees with theoretical results. Our study provides an approach of localizing the subwavelength acoustic wave.
The recent discovery of higher-order topological insulators (TIs) has opened new possibilities in the search for novel topological materials and metamaterials. Second-order TIs have been implemented in two-dimensional (2D) systems exhibiting topological corner states, as well as three-dimensional (3D) systems having one-dimensional (1D) topological hinge states. Third-order TIs, which have topological states three dimensions lower than the bulk (which must thus be 3D or higher), have not yet been reported. Here, we describe the realization of a third-order TI in an anisotropic diamond-lattice acoustic metamaterial. The bulk acoustic bandstructure has nontrivial topology characterized by quantized Wannier centers. By direct acoustic measurement, we observe corner states at two corners of a rhombohedron-like structure, as predicted by the quantized Wannier centers. This work extends topological corner states from 2D to 3D, and may find applications in novel acoustic devices.
The three dimensional (3D) topological insulators are predicted to exhibit a 3D Dirac semimetal state in critical regime of topological to trivial phase transition. Here we demonstrate the first experimental evidence of 3D Dirac semimetal state in topological insulator Bi2Se3 with bulk carrier concentration of ~ 10^19 cm^{-3}, using magneto-transport measurements. At low temperatures, the resistivity of our Bi2Se3 crystal exhibits clear Shubnikov-de Haas (SdH) oscillations above 6T. The analysis of these oscillations through Lifshitz-Onsanger and Lifshitz-Kosevich theory reveals a non-trivial pi Berry phase coming from 3D bands, which is a decisive signature of 3D Dirac semimetal state. The large value of Dingle temperature and natural selenium vacancies in our crystal suggest that the observed 3D Dirac semimetal state is an outcome of enhanced strain field and weaker effective spin-orbit coupling.
Topological boundary and interface modes are generated in an acoustic waveguide by simple quasi-periodic patternings of the walls. The procedure opens many topological gaps in the resonant spectrum and qualitative as well as quantitative assessments of their topological character are supplied. In particular, computations of the bulk invariant for the continuum wave equation are performed. The experimental measurements reproduce the theoretical predictions with high fidelity. In particular, acoustic modes with high Q-factors localized in the middle of a breathable waveguide are engineered by a simple patterning of the walls.
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