Topologically Protected Transport in Engineered Mechanical Systems

Over the past decade, there has been a great interest in topological effects, with concepts originally developed in the context of electron transport in condensed matter platforms now being extended to optical systems. While topological properties in electronic systems are often linked to the quantization of electric conductivity observed in the integer quantum Hall effect, a direct analogue in optics remains elusive. In this study, we bridge this gap by demonstrating that th...

Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in active matter through experimentally relevant examples. Here, the focus lies on topological defects and topologically protected edge modes with an emphasis on the distinctive properties they acquire in active media. These paradigmatic examp...

Topological pumping supplies a robust mechanism to steer waves across a sample without being affected by disorders and defects. For the first time, we demonstrate the pumping of elastic surface waves, achieved by a smart patterning of a surface that creates a synthetic dimension, which is explored by the wave as it is launched perpendicularly to the steering direction. Specifically, we design and fabricate an elastic medium decorated with arrays of pillar-type resonators whos...

The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics, designating a material as insulating or conducting amounts to asking if it is rigid or floppy. Although mechanical structures that display topological floppy modes have been proposed, they are all vulnerable to global collapse. Here, we design and build mechanical metamaterials that ar...

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 experimental characterization of topological kagome lattices, aimed at elucidating their in-plane phononic and topological characteristics. We specifically explore the continuum elasticity limit, which is established when the ideal hinges that appear...

Topological mechanics can realize soft modes in mechanical metamaterials in which the number of degrees of freedom for particle motion is finely balanced by the constraints provided by interparticle interactions. However, solid objects are generally hyperstatic (or overconstrained). Here, we show how symmetries may be applied to generate topological soft modes even in overconstrained, rigid systems. To do so, we consider non-Hermitian topology based on non-square matrices, an...

Guiding energy deliberately is one of the central elements in engineering and information processing. It is often achieved by designing specific transport channels in a suitable material. Topological metamaterials offer a way to construct stable and efficient channels of unprecedented versatility. However, due to their stability it can be tricky to terminate them or to temporarily shut them off without changing the material properties massively. While a lot of effort was put ...

Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic, electromagnetic and mechanical transport properties across a wide range of systems, from cold atoms to metamaterials, active matter and geophysical flows. Recently, the advent of non-Hermitian topological systems---wherein energy is not conserved-...

We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a controllable way, simply by changing the contact angles between the cylinders. The spatial variation of particles' stiffness results in an in-situ transition of the system's topology. This manifests as the emergence of a boundary mode in the...

Recent progress in topological mechanics have revealed a family of Maxwell lattices that exhibit topologically protected floppy edge modes. These modes lead to a strongly asymmetric elastic wave response. In this paper, we show how topological Maxwell lattices can be used to realize non-reciprocal transmission of elastic waves. Our design leverages the asymmetry associated with the availability of topological floppy edge modes and the geometric nonlinearity built in the mecha...