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 …

Most natural and artificial materials have crystalline structures from which abundant
topological phases emerge,,,,–. However, the bulk–edge correspondence—which has been …

Gauge fields play a major role in understanding quantum effects. For example, gauge flux
insertion into single unit cells is crucial towards detecting quantum phases and controlling …

Optical vector vortex beams provide additional degrees of freedom for spatially
distinguishable channels in data transmission. Although several coherent light sources …

Topological crystalline insulators (TCIs) can exhibit unusual, quantized electric phenomena
such as fractional electric polarization and boundary-localized fractional charge,,,,–. This …

Topological phases of matter have been extensively investigated in solid-state materials and
classical wave systems with integer dimensions. However, topological states in non-integer …

We investigate higher-order Weyl semimetals (HOWSMs) having bulk Weyl nodes attached
to both surface and hinge Fermi arcs. We identify a new type of Weyl node, which we dub a …

The orbital degrees of freedom play a pivotal role in understanding fundamental
phenomena in solid-state materials as well as exotic quantum states of matter including …