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 …

The concept of topological energy bands and their manifestations have been demonstrated
in condensed matter systems as a fantastic paradigm toward unprecedented physical …

In solid state physics, a bandgap (BG) refers to a range of energies where no electronic
states can exist. This concept was extended to classical waves, spawning the entire fields of …

Pursuing topological phases in natural and artificial materials is one of the central topics in
modern physical science and engineering. In classical magnetic systems, spin waves (or …

Energy in lower dimensions, such as edges or corners, can be robustly confined by the
higher-order topological insulators (HOTIs) against defects. Being promising for wave …

Photonic and phononic topological insulators (TIs) offer numerous opportunities for
manipulating light and sound with high efficiency and resiliency. On the other hand, inverse …

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 …

Second-order elastic topological insulators (SETIs) with topologically protected corner states
offer new routes for the realization of the robust manipulation of elastic waves in lower …

Recently, higher-order topological insulators (HOTIs) as a novel frontier of topological
phases of matter have been induced in mechanical systems, opening new routes to …

Higher-order topological insulators (HOTIs), capable of hosting topological states over
multiple dimensionalities, have received considerable attention recently, providing …