Related papers: Universal Continuum Theory for Topological Edge So…

In the past a few years, topologically protected mechanical phenomena have been extensively studied in discrete lattices and networks, leading to a rich set of discoveries such as topological boundary/interface floppy modes and states of…

In floppy mechanical lattices, robust edge states and bulk Weyl modes are manifestations of underlying topological invariants. To explore the universality of these phenomena independent of microscopic detail, we formulate topological…

Continuum lattice grid structures which consist of joined elastic beams subject to flexural deformations are ubiquitous. In this work, we establish a theoretical framework of the topological dynamics of continuum lattice grid structures,…

Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…

Boundaries in gauge theory and gravity give rise to symmetries and charges at both finite and asymptotic distance. Due to their structural similarities, it is often held that soft modes are some kind of asymptotic limit of edge modes. Here,…

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…

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…

Although topological mechanical metamaterials have been extensively studied from a theoretical perspective, their experimental characterization has been lagging. To address this shortcoming, we present a systematic laser-assisted…

Topological mechanical metamaterials have demonstrated exotic and robust mechanical properties which led to promising engineering applications. One of such properties is the focusing of stress at the interface connecting domains of…

Topology describes global quantities invariant under continuous deformations, such as the number of elementary excitations at a phase boundary, without detailing specifics. Conversely, differential laws are needed to understand the physical…

Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously…

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…

We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with…

We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry protected topological phases. This is possible even without gapped degrees of freedom in the bulk ---in…

Mechanical metamaterials are those structures designed to convey force and motion in novel and desirable ways. Recently, Kane and Lubensky showed that lattices at the point of marginal mechanical stability (Maxwell lattices) possess a…

Maxwell lattices are characterized by an equal number of degrees of freedom and constraints. A subset of them, dubbed topological lattices, are capable of localizing stress and deformation on opposing edges, displaying a polarized…

Finite topologically non-trivial systems are often characterised by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain…

The study of topological states in electronic structures, which allows robust transport properties against impurities and defects, has been recently extended to the realm of elasticity. This work shows that nontrivial topological flexural…

Topological mechanical structures exhibit robust properties protected by topological invariants. In this letter, we study a family of deformed square lattices that display topologically protected zero-energy bulk modes analogous to the…

The topological band theory predicts that bulk materials with nontrivial topological phases support topological edge states. This phenomenon is universal for various wave systems and has been widely observed for electromagnetic and acoustic…