A comparison study between acoustic topological states based on valley Hall and quantum spin Hall effects

Abstract

Over the past few years, the rapid development in the fields of condensed matter physics, electronic, and photonic systems have inspired the design and experimental demonstration of various acoustic topological insulators (TIs). Among these, the topologically protected one-way propagation is a phenomenon that is gaining increased attention. Pseudospin states, which is the analogue of the quantum spin Hall effect from electronic systems, has been proven to enable topological edge states in acoustics. Similarly, the valley Hall (VH) effect is also observed in acoustic systems and provides a pair of valley vortex states with opposite chirality. These valley vortex states can similarly form topologically protected edge states and, in turn, realize robust one-way propagation. However, the differences in the physics behind these acoustic systems give rise to distinct features such as different angle selections and immunization levels to various types of defects. This article conducts a comparison study between topological states in valley Hall phononic crystals and TIs that reveals the differences and similarities in several aspects. Both of them have topologically protected edge states and thus the robust one-way propagation. For the maximum transmission incident angle and defect immunization, however, VH topological waveguides and TI waveguides show different characteristics.

Topological states in twisted pillared phononic plates

“…Orazbayev and Fleury quantitatively analyzed topological edge modes in photonic crystals with zigzag, bridge and armchair interfaces and compared them in spin-Hall and valley-Hall insulators showing the importance of the specific edge on the robustness [28]. Deng et al systematically studied the angle dependence of topologically protected armchair edge states and revealed the difference and similarities to spin-Hall and valley-Hall effect designs [29]. For the platform of phononic plates [30][31][32][33][34], it is possible to design a phononic plate with double sided pillars and further twist the double layers as a Moiré pattern.…”

Synthetic Kramers Pair in Phononic Elastic Plates and Helical Edge States on a Dislocation Interface

“…Nevertheless, it was reported that phononic systems exploiting this mechanism could give rise to gapped edge states at zero momentum where the ω– dispersion curves of the counter‐propagating edge states repel each other, due to coupling between them. [ 21–31 ] These results showed that the edge states are not a Kramers pair and do not have a continuous spectrum across the bulk band gap. In addition, although the zone‐folding approach is already widely adopted, previous studies concentrated on mapping the system back to the electronic counterpart but usually omitted explaining some discrepancies between the synthetic phononic pseudospins and the electron's intrinsic spin; hence, leaving behind some obscure points such as the indeterminate pseudospin states, and the seemingly indistinguishable topological phases.…”

“…However, these systems required the breaking of time reversal symmetry (TRS), which imposes significant practical complexities due to the need for either special magneto‐optic and elastic materials, or for carefully controlled external input. [ 9–18 ] More recently, mechanisms analog to TRS‐preserved quantum spin Hall effect (QSHE) [ 19–34 ] and quantum valley Hall effect [ 31,35–46 ] were also proposed. These systems could be built based on ordinary dielectric or linearly elastic materials, and only required the breaking of spatial symmetry, which was a considerably more practical approach.…”

“…Researchers have proposed different ideas to synthesize properties analog to electron spins, often referred to as “pseudospins”. In phononic elastic systems, examples include mixing of symmetric and antisymmetric Lamb modes in waveguides, [ 33,34 ] and a “zone‐folding” method [ 21–32 ] to attain a doubly degenerate Dirac cone at the center of the Brillouin zone that acts as a degree of freedom that resembles electron spins. Nevertheless, it was reported that phononic systems exploiting this mechanism could give rise to gapped edge states at zero momentum where the ω– dispersion curves of the counter‐propagating edge states repel each other, due to coupling between them.…”

Coupled acoustic resonator systems with novel acoustic properties

“…Now we can conclude that the propagation of such kind valley edge states along the domain wall is only supported at a zigzag domain wall, as predicted in gapped graphene (100). There was a work where valley Hall edge states were found along armchair domain walls (101). Actually, there will be a gap between the edge states for armchair interfaces, but with some specifically geometry design, the mix between the projections of the valleys and ′ on the interface might be such weak that the gap between the edge states is negligible, leading to the propagating edges states along the armchair interfaces.…”