We demonstrate that higher-order topological insulators with C4 symmetry can be realized in two-dimensional elastic phononic crystals. Both one-dimensional topological edge states and zero-dimensional topological corner states are visualized and can transform each other by tuning the crystalline symmetry in a hierarchical structure. The systematic band structure calculations indicate that elastic wave energy in the hierarchical structures can be localized with remarkable robustness, which is very promising for new generations of integrated solid-state phononic circuits with a great versatility. In addition, the corner states residing in a much wider bandgap greatly increase the signal-to-noise ratio of topological devices.
Recently, the concept of valley pseudospin, labeling quantum states of energy extrema in momentum space, has attracted enormous attention because of its potential as a new type of information carrier. Here, we present surface acoustic wave (SAW) waveguides, which utilize and transport valley pseudospins in two-dimensional SAW phononic crystals (PnCs). In addition to a direct visualization of the valley-dependent states excited from the corresponding chiral sources, the backscattering suppression of SAW valley-dependent edge states transport is observed in sharply curved interfaces. By means of band structure engineering, elastic wave energy in the SAW waveguides can be transported with remarkable robustness, which is very promising for new generations of integrated solid-state phononic circuits with great versatility.Valley, an intriguing and significant concept in condensed matter physics, stems from the extensive research of two dimensional (2D) hexagonal crystals, such as graphene, bilayer graphene, and transition-metal dichalcogenides, in recent years. [1][2][3][4][5][6][7][8][9][10][11][12][13] When the inversion symmetry is broken in two-dimensional (2D) hexagonal lattices, the berry curvatures will acquire opposite signs at K and K' points due to time-reversal symmetry. Subsequently, the electrons in different valleys own opposite anomalous velocities and move towards the opposite directions. Additionally, slow valley relaxation and dephasing processes, compared to electron spin, can be accessed due to the reason that intervalley scattering is suppressed by large momentum separation between different valleys. 2,3,12,14
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