Topological acoustics is an emerging field that lies at the intersection of condensed matter
physics, mechanical structural design and acoustics engineering. It explores the design and …

A conventional topological insulator (TI) has gapped bulk states but gapless edge states.
The emergence of the gapless edge states is dictated by the bulk topological invariant of the …

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 …

Topological features embedded in ancient braiding and knotting arts endow significant
impacts on our daily life and even cutting-edge science. Recently, fast growing efforts are …

Phononic crystals (PnCs) control the transport of sound and heat similar to the control of
electric currents by semiconductors and metals or light by photonic crystals. Basic and …

Weyl semimetals (WSMs) exhibit phenomena such as Fermi arc surface states, pseudo-
gauge fields and quantum anomalies that arise from topological band degeneracy in …

Higher-order topology yields intriguing multidimensional topological phenomena, while
Weyl semimetals have unconventional properties such as chiral anomaly. However, so far …

The notion of higher-order topological insulators has endowed materials with topological
states beyond the first order. Particularly, a three-dimensional (3D) higher-order topological …

Higher-order topological phases have raised widespread interest in recent years with the
occurrence of the topological boundary states of dimension two or more less than that of the …

Topological phases of matter have attracted significant attention in recent years, due to the
unusual robustness of their response to defects and disorder. Various research efforts have …