Mirror-symmetry induced topological valley transport along programmable boundaries in a hexagonal sonic crystal

Abstract

Valley states, labeling the frequency extrema in momentum space, carry a new degree of freedom (valley pseudospin) for topological transport of sound in sonic crystals. Recently, the field of valley acoustics has become a hotspot due to its potentials in developing various topological-insulator-based devices. In most previous works, topological valley transport is implemented at the interfaces of two connected artificial crystals. With respect to the interface, the mirror symmetry of crystal structures supports either even-mode or odd-mode valley states. In this work, we propose a physical insight of transforming one hexagonal crystal into a virtual lattice by utilizing the mirror operation of rigid or soft boundaries, which greatly reduces the dimension of the acoustic structure and provides a possible way to implement the programmable routing of topological propagation. We investigate two cases that the rigid and soft boundaries are introduced either at the edge or inside a single hexagonal crystal. Our results clearly demonstrate the high-transmission valley transport along the folded boundaries, where reflection or scattering is prohibited at the sharp bending or corners due to topological protection. Three functional devices are exemplified, which are single-crystal-based topological delay-line filter, delay-line switcher and beam splitter. Our work reveals the inherent relation between the field symmetries of valley states and structural symmetries of sonic crystals. Programmable routing of topological sound transport through boundary engineering provides a platform for developing integrated and versatile topological-insulator-based devices.

Higher-order valley vortices enabled by synchronized rotation in a photonic crystal

“…Thus topological switches by valley selection of corner states are numerically demonstrated in our paper. Our valley HOTI and the valley-selective corner states provide fundamental understanding on the interplay between higher-order topology and valley degree of freedom, which may find potential applications in valleytronics for future information carriers, such as waveguides, couplers and topological circuit switches in THz regime [24,30,[38][39][40][41][42][43].…”

Acoustic transport in higher-order topological insulators with Dirac hierarchy

“…The discovery of topological insulators (TIs) has provided novel opportunities for advances in the research on condensed matter physics and material science [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The concept of higher-order topological insulators (HOTIs)-a new category of TIs-originated from quantum electronic systems [16][17][18].…”

Dual-band all-dielectric chiral photonic crystal

“…The topological insulator [4][5][6] is a quantum state with internal insulation and surface conductivity [7,8], which can exhibit topologically protected edge states. Recently, topological insulators have been extended to further areas of mechanics [9][10][11][12][13][14], acoustics [15][16][17][18][19][20][21][22], photonic [23][24][25][26][27][28] and electronics [29] with particular interests focusing on achieving * Authors to whom any correspondence should be addressed.…”