Subwavelength and directional control of flexural waves in zone-folding induced topological plates

Abstract

Inspired by the quantum spin Hall effect shown by topological insulators, we propose a plate structure that can be used to demonstrate the pseudo-spin Hall effect for flexural waves. The system consists of a thin plate with periodically arranged resonators mounted on its top surface. We extend a technique based on the plane wave expansion method to identify a double Dirac cone emerging due to the zone-folding in frequency band structures. This particular design allows us to move the double Dirac cone to a lower frequency than the resonating frequency of local resonators. We then manipulate the pattern of local resonators to open subwavelength Bragg band gaps that are topologically distinct. Building on this method, we verify numerically that a waveguide at an interface between two topologically distinct resonating plate structures can be used for guiding low-frequency, spin-dependent one-way flexural waves along a desired path with bends. PACS numbers: 45.70.-n 05.45.-a 46.40.Cd

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

“…This has culminated in the consolidation of topological mechanics [10] and acoustics [11] as active research fields [12]. Topological states have been successfully observed in several platforms [13][14][15][16][17][18][19][20][21], and have been pursued to achieve robust, diffraction-free wave motion. Additional functionalities have been explored in the context of topological pumping [22][23][24][25][26], quasi-periodicity [27][28][29], and non-reciprocal wave propagation in active [30][31][32][33][34][35][36] or passive non-linear [37][38][39][40] systems.…”

Mechanical Analogue of a Majorana Bound State

“…As an example of the latter, artificial gyroscopic lattices have been shown to sustain robust chiral edge states by mimicking the quantum Hall effect . Other phononic metamaterials have been constructed to enable mechanical versions of the quantum spin Hall effect and the valley degree of freedom for unidirectional phononic signal guiding.…”

“…As an example of the latter, artificial gyroscopic lattices have been shown to sustain robust chiral edge states by mimicking the quantum Hall effect. [3,4] Other phononic metamaterials have been constructed to enable mechanical versions of the quantum spin Hall effect [5][6][7] and the valley degree of freedom [8] for unidirectional phononic signal guiding.Topological modes at an extended boundary are propagating, but this is not generic. Prominent examples of bound states have been reported in Maxwell lattices for static floppy modes, [2,9] 1D spring-connected dimer chains, [10] and photonic Majorana zero-mode crystals.…”

“…This gives rise to Dirac-like flexural modes, i.e., a kind of mechanical graphene. [6,34,35] The vortex is then realized by deforming the honeycomb pattern following a Kekulé distortion. [36] The resulting pattern of bolts, honeycomb plus distortion, is rendered in Figure 1.…”

2D Phononic Crystals: Progress and Prospects in Hypersound and Thermal Transport Engineering

“…Breaking the time‐reversal symmetry to obtain an equivalent to the quantum Hall effect in bosonic lossless systems requires active materials responding to an external field, a nonlinearity, or time‐dependent physical properties, which in the case of elasticity is especially difficult. Therefore, several proposals, as well as few experimental realizations, have achieved topological phenomena by emulating the quantum spin Hall effect or quantum valley Hall effect in passive linear structures. While conserving time‐reversal symmetry, these topological structures are based on breaking some spatial inversion symmetry.…”