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Abstract Topological mechanical metamaterials have been widely explored for their boundary states, which can be robustly isolated or transported in a controlled manner. However, such systems often require pre-configured design or complex active actuation for wave manipulation. Here, we present the possibility of in-situ transfer of topological boundary modes by leveraging the reconfigurability intrinsic in twisted origami lattices. In particular, we employ a dimer Kresling origami system consisting of unit cells with opposite chirality, which couples longitudinal and rotational degrees of freedom in elastic waves. The quasi-static twist imposed on the lattice alters the strain landscape of the lattice, thus significantly affecting the wave dispersion relations and the topology of the underlying bands. This in turn facilitates an efficient topological state transfer from one edge to the other. This simple and practical approach to energy transfer in origami-inspired lattices can thus inspire a new class of efficient energy manipulation devices. 

Abstract Demonstration of topological boundary modes in elastic systems has attracted a great deal of attention over the past few years due to its unique protection characteristic. Recently, second-order topological insulators have been proposed in manipulating the topologically protected localized states emerging only at corners. Here, we numerically and experimentally study corner states in a two-dimensional phononic crystal, namely a continuous elastic plate with embedded bolts in a hexagonal pattern. We create interfacial corners by adjoining trivial and non-trivial topological configurations. Due to the rich interaction between the bolts and the continuous elastic plate, we find a variety of corner states of and devoid of topological origin. Strikingly, some of the corner states are not only highly-localized but also tunable. Taking advantage of this property, we experimentally demonstrate asymmetric corner localization in a Z-shaped domain wall. This finding could create interest in exploration of tunable corner states for the use of advanced control of wave localization. 

Abstract The discovery of topologically nontrivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most remarkable and robust phases in electronic systems (e.g., quantum Hall or anomalous quantum Hall) are the result of topological protection. These powerful ideas have recently begun to be explored also in bosonic systems. Topologically protected acoustic, mechanical, and optical edge states have been demonstrated in a number of systems that recreate the requisite topological conditions. Such states that propagate without backscattering could find important applications in communications and energy technologies. Here, a topologically bound mechanical state, a different class of nonpropagating protected state that cannot be destroyed by local perturbations, is demonstrated. It is in particular a mechanical analogue of the well‐known Majorana bound states (MBSs) of electronic topological superconductor systems. The topological binding is implemented by creating a Kekulé distortion vortex on a 2D mechanical honeycomb superlattice that can be mapped to a magnetic flux vortex in a topological superconductor.