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Metamaterials are engineered materials composed of specially designed unit cells that exhibit extraordinary properties beyond those of natural materials. Complex engineering tasks often require heterogeneous unit cells to accommodate…
The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from three different points of view. Specifically tools for multiple scattering theory, functional analysis, differential geometry and…
Rapid advances in additive manufacturing over the past decade have kindled widespread interest in the rational design of metamaterials with unique properties. However, many applications require multi-physics metamaterials, where multiple…
In recent decades, scientists have developed the means to engineer synthetic periodic arrays with feature sizes below the wavelength of light. When such features are appropriately structured, electromagnetic radiation can be manipulated in…
Recent advances in hyperbolic metamaterials have spurred many breakthroughs in the field of manipulating light propagation. However, the unusual electromagnetic properties also put extremely high demands on its compositional materials.…
Seeing sharper or becoming invisible are visions strongly driving the development of THz metamaterials. Strings are a preferred architecture of metamaterials as they extend continuously along one dimension. Here, we demonstrate that…
Mechanical metamaterials -- structures with unusual properties that emerge from their internal architecture -- that are designed to undergo large deformations typically exploit large internal rotations, and therefore, necessitate the…
Structures with artificial mechanical properties, often called mechanical metamaterials, exhibit divergent yet tunable performance. Various types of mechanical metamaterials have been proposed, which harness light or magnetic interactions,…
Metamaterials with floppy modes called mechanisms are a burgeoning template for shape-morphing systems and structures across scales. Here, we present a design recipe that transforms an arbitrary plane tiling into a 2D kirigami pattern with…
Defects, and in particular topological defects, are architectural motifs that play a crucial role in natural materials. Here we provide a systematic strategy to introduce such defects in mechanical metamaterials. We first present…
Concepts from quantum topological states of matter have been extensively utilized in the past decade in creating mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized…
Spatial tailoring of the material constitutive properties is a well-known strategy to mold the local flow of given observables in different physical domains. Coordinate-transformation-based methods (e.g., transformation optics) offer a…
A supersolid is a system that presents long-range order and shear rigidity as a solid but which also supports a non-dissipative superflow as a superfluid. From an effective perspective, supersolids are identified with phases of matter that…
Multi-step pathways, constituted of a sequence of reconfigurations, are central to a wide variety of natural and man-made systems. Such pathways autonomously execute in self-guided processes such as protein folding and self-assembly, but…
Gauging is a general procedure for mapping a quantum many-body system with a global symmetry to one with a local gauge symmetry. We consider a generalized gauging map that does not enforce gauge symmetry at all lattice sites, and show that…
Mechanical metamaterials are engineered materials that gain their remarkable mechanical properties, such as negative Poisson's ratios, negative compressibility, phononic bandgaps, and topological phonon modes, from their structure rather…
Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain noncompact $3-$folds, called building blocks, satisfying a stability condition `at infinity'. Such bundles are known to…
We present an analytical framework to describe the complex nonlinear response of two-dimensional porous mechanical metamaterials. We adopt a geometric approach to elasticity in which pores are represented by elastic charges, and show that…
Metamaterials benefit from unique architected patterns to achieve lightweight with exceptional mechanical properties inaccessible to conventional materials. Typical mechanical metamaterials are inspired by crystal-like lattice structures,…
Holographic quantum error correcting codes (HQECC) have been proposed as toy models for the AdS/CFT correspondence, and exhibit many of the features of the duality. HQECC give a mapping of states and observables. However, they do not map…