Edge states and topological pumping in stiffness-modulated elastic plates

Abstract

We demonstrate that modulations of the stiffness properties of an elastic plate along a spatial dimension induce edge states spanning non-trivial gaps characterized by integer valued Chern numbers. We also show that topological pumping is induced by smooth variations of the phase of the modulation profile along one spatial dimension, which results in adiabatic edge-to-edge transitions of the edge states. The concept is first illustrated numerically for sinusoidal stiffness modulations, and then experimentally demonstrated in a plate with square-wave thickness profile. The presented numerical and experimental results show how continuous modulations of properties may be exploited in the quest for topological phases of matter. This opens new possibilities for topology-based waveguiding through slow modulations along a second dimension, spatial or temporal.

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

“…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. These works and the references therein illustrate a wealth of strategies for the manipulation of elastic and acoustic waves, and suggest intriguing possibilities for technological applications in acoustic devices, sensing, energy harvesting, among others.…”

Progress in Topological Mechanics

“…In parallel with the development of the QHE, a new perspective, a topological pump, has been proposed to investigate topologically protected modes [20,[118][119][120][121][122][123]. The topological pump exploits synthetic dimensions mapped to time [123][124][125][126][127] or space [24,119,120,[128][129][130][131], controlling the generation and transition of topological states. The synthetic dimensions refer to exploring higher-dimensional physics with virtual dimensions in lowerdimensional systems.…”

“…Recently, the topological pump in elastic systems has been demonstrated theoretically and experimentally [124,126,128,130,[135][136][137]. In 2019, Rosa et al firstly theoretically demonstrated the topological pump in spatially modulated elastic lattices [128].…”

Topological pumping in acoustic waveguide arrays with hopping modulation

“…On the other hand, the time-dependent Schrödinger equation and the paraxial wave equation share a similar mathematical form. This fact has been leveraged for the realization of Thouless pumping by mapping the temporal evolution to the spatial dimension along the propagative direction [18,19,[23][24][25][26][27][28][29][30][31]. Very recently, both onsite [23] and hopping [31] modulation strategies have been developed in acoustic waveguide systems to explore the propagating effects of topological edge states.…”