Topological Phase Transition in a One-Dimensional Elastic String System

Topological Metamaterials

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 variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

Recent advances in topological elastic metamaterials

Topological elastic metamaterials have emerged as a new frontier in the quest of topological phases in condensed matter physics. Their exotic topological properties open a wealth of promising engineering-oriented applications that are difficult to realize with traditional elastic metamaterials, such as robust and defect insensitive waveguiding, signal sensing, and splitting. In this review, we retrospectively examine the underlying physical concept of topologically ordered states of elastic waves, starting from the one-dimensional example based on the Su-Schrieffer-Heeger model. We then move on to two-dimensional topological metamaterials, discussing elastic analogues of quantum Hall, pseudospin-Hall, valley-Hall phases. Finally, we survey the latest developments in the field including three-dimensional elastic topological phases and higher-order topological insulators. Altogether, this paper provides a comprehensive overview of the flourishing research frontier on topological elastic metamaterials, and highlights prominent future directions in this field.