Topological Metamaterials

Abstract

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.

Elastic metamaterials for guided waves: from fundamentals to applications

“…The dispersion relation in figure 19(b) shows that double Dirac cones and topological CBGs are formed near the resonance frequency of the bolts. The design principle and recent advances in topological elastic metamaterials are comprehensively reviewed in [55,56,331].…”

Valley edge states with opposite chirality in temperature dependent acoustic media

“…The field of acoustic topological QVHE is experiencing rapid advancement due to its adaptability and variety, offering a new avenue for manipulating the propagation of acoustic waves [23][24][25][26][27]. Numerous captivating subjects related to valley properties have been explored, such as topological oneway edge states [2,3,28], acoustic topological insulators [29,30], acoustic topological rainbow trapping [31,32] and topological valley transport [14,33,34].…”

Coexistence of Long-Range Magnetic Order and Magnetic Frustration of a Novel Two-Dimensional S = 1/2 Structure: Na2Cu3(SeO3)4

“…The pursuit of quantum materials (QMs) is driven both by a fundamental interest in their exotic physics and by the imminent practicality of their emergent properties, which may usher in a new era of quantum device designs [1][2][3]. The scientific interest is largely driven by the potential to isolate new forms of matter that are predicted to host novel physical properties among the nonclassical phases, including those of quantum spin liquids (QSLs), emergent topological states, spin-orbit coupled metals, Dirac semi-metals, Weyl semi-metals, topological Mott insulators, and topological axion insulators [3][4][5][6]. One of the most important factors influencing the development of quantum materials research is that of the ability of inorganic and materials chemists to grow high-quality single crystals [3].…”