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 …

There are two prominent applications of the mathematical concept of topology to the physics
of materials: band topology, which classifies different topological insulators and semimetals …

Light and sound are the most ubiquitous forms of waves, associated with a variety of
phenomena and physical effects such as rainbows and echoes. Light and sound, both …

In active matter systems, individual constituents convert energy into non-conservative forces
or motion at the microscale, leading to morphological features and transport properties that …

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

Topological quantum chemistry and symmetry-based indicators have facilitated large-scale
searches for materials with topological properties at the Fermi energy (EF). We report the …

In the presence of crystalline symmetries, certain topological insulators present a filling
anomaly: a mismatch between the number of electrons in an energy band and the number of …

What are topological phases of matter? First, they are phases of matter at zero temperature.
Second, they have a nonzero energy gap for the excitations above the ground state. Third …

We present a method for efficiently enumerating all allowed, topologically distinct, electronic
band structures within a given crystal structure in all physically relevant dimensions. The …

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