The topological properties of an object, associated with an integer called the topological
invariant, are global features that cannot change continuously but only through abrupt …

Topological mechanical metamaterials have emerged with the development of topological
phases and topological phase transitions in modern condensed matter physics. Their …

Transition fronts, moving through solids and fluids in the form of propagating domain or
phase boundaries, have recently been mimicked at the structural level in bistable …

Concepts from quantum topological states of matter have been extensively utilized in the
past decade to create mechanical metamaterials with topologically protected features, such …

Topological surface states are unique to topological materials and are immune to
disturbances. In isostatic lattices, mechanical topological floppy modes exhibit softness …

The concepts of origami and kirigami have often been presented separately. Here, we put
forth a synergistic approach—the folded kirigami—in which kirigami assemblies are …

Here we review recent studies of mechanical metamaterials originating from or closely
related to marginally jammed solids. Unlike previous approaches mainly focusing on the …

Soft materials can self-assemble into highly structured phases that replicate at the
mesoscopic scale the symmetry of atomic crystals. As such, they offer an unparalleled …

Originally discovered in condensed matter systems, topological insulators (TIs) have been
ubiquitously extended to various fields of classical wave physics including photonics …

Mechanical metamaterials are designed to exhibit enhanced properties not found in natural
materials or to bolster the properties of existing materials. The theoretical foundations for …