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Maxwell lattices possess distinct topological states that feature mechanically polarized edge behaviors and asymmetric dynamic responses protected by the topology of their phonon bands. Until now, demonstrations of non‐trivial topological behaviors from Maxwell lattices have been limited to fixed configurations or have achieved reconfigurability using mechanical linkages. Here, a monolithic transformable topological mechanical metamaterial is introduced in the form of a generalized kagome lattice made from a shape memory polymer (SMP). It is capable of reversibly exploring topologically distinct phases of the non‐trivial phase space via a kinematic strategy that converts sparse mechanical inputs at free edge pairs into a biaxial, global transformation that switches its topological state. All configurations are stable in the absence of confinement or a continuous mechanical input. Its topologically‐protected, polarized mechanical edge stiffness is robust against broken hinges or conformational defects. More importantly, it shows that the phase transition of SMPs that modulate chain mobility, can effectively shield a dynamic metamaterial's topological response from its own kinematic stress history, referred to as “stress caching”. This work provides a blueprint for monolithic transformable mechanical metamaterials with topological mechanical behavior that is robust against defects and disorder while circumventing their vulnerability to stored elastic energy, which will find applications in switchable acoustic diodes and tunable vibration dampers or isolators.

 

Self-organized complex structures in nature, e.g., viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality. Can we program the self-assembly of three-dimensional (3D) complex structures using simple building blocks, and reach similar or higher level of sophistication in engineered materials? Here we present an analytic theory for the self-assembly of polyhedral nanoparticles (NPs) based on their crystal structures in non-Euclidean space. We show that the unavoidable geometrical frustration of these particle shapes, combined with competing attractive and repulsive interparticle interactions, lead to controllable self-assembly of structures of complex order. Applying this theory to tetrahedral NPs, we find high-yield and enantiopure self-assembly of helicoidal ribbons, exhibiting qualitative agreement with experimental observations. We expect that this theory will offer a general framework for the self-assembly of simple polyhedral building blocks into rich complex morphologies with new material capabilities such as tunable optical activity, essential for multiple emerging technologies.

 

Exciton dynamics can be strongly affected by lattice vibrations through electron-phonon coupling. This is rarely explored in two-dimensional magnetic semiconductors. Focusing on bilayer CrI₃, we first show the presence of strong electron-phonon coupling through temperature-dependent photoluminescence and absorption spectroscopy. We then report the observation of periodic broad modes up to the 8th order in Raman spectra, attributed to the polaronic character of excitons. We establish that this polaronic character is dominated by the coupling between the charge-transfer exciton at 1.96 eV and a longitudinal optical phonon at 120.6 cm⁻¹. We further show that the emergence of long-range magnetic order enhances the electron-phonon coupling strength by ~50% and that the transition from layered antiferromagnetic to ferromagnetic order tunes the spectral intensity of the periodic broad modes, suggesting a strong coupling among the lattice, charge and spin in two-dimensional CrI₃. Our study opens opportunities for tailoring light-matter interactions in two-dimensional magnetic semiconductors.

 

Periodic networks on the verge of mechanical instability, called Maxwell lattices, are known to exhibit zero-frequency modes localized to their boundaries. Topologically polarized Maxwell lattices, in particular, focus these zero modes to one of their boundaries in a manner that is protected against disorder by the reciprocal-space topology of the lattice’s band structure. Here, we introduce a class of mechanical bilayers as a model system for designing topologically protected edge modes that couple in-plane dilational and shearing modes to out-of-plane flexural modes, a paradigm that we refer to as “omnimodal polarization.” While these structures exhibit a high-dimensional design space that makes it difficult to predict the topological polarization of generic geometries, we are able to identify a family of mirror-symmetric bilayers that inherit the in-plane modal localization of their constitutive monolayers, whose topological polarization can be determined analytically. Importantly, the coupling between the layers results in the emergence of omnimodal polarization, whereby in-plane and out-of-plane edge modes localize on the same edge. We demonstrate these theoretical results by fabricating a mirror-symmetric, topologically polarized kagome bilayer consisting of a network of elastic beams via additive manufacturing and confirm this finite-frequency polarization via finite element analysis and laser-vibrometry experiments.

 

Recent advances in topological mechanics have revealed unusual phenomena such as topologically protected floppy modes and states of self-stress that are exponentially localized at boundaries and interfaces of mechanical networks. In this paper, we explore the topological mechanics of epithelial tissues, where the appearance of these boundary and interface modes could lead to localized soft or stressed spots and play a role in morphogenesis. We consider both a simple vertex model (VM) governed by an effective elastic energy and its generalization to an active tension network (ATN) which incorporates active adaptation of the cytoskeleton. By analyzing spatially periodic lattices at the Maxwell point of mechanical instability, we find topologically polarized phases with exponential localization of floppy modes and states of self-stress in the ATN when cells are allowed to become concave, but not in the VM.