Thouless pum** provides one of the simplest manifestations of topology in quantum
systems and has attracted a lot of recent interest, both theoretically and experimentally …

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 topological protection of wave transport, originally observed in the context of the
quantum Hall effect in two-dimensional electron gases, has been shown to apply broadly to …

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

In many contexts, interaction between particles gives rise to emergent phenomena. An
example is the fractional quantum Hall effect, where the interaction between electrons leads …

Exploring the interplay between topological band structures and tunable nonlinearities has
become possible with the development of synthetic lattice systems. In this emerging field of …

Topological pumps have garnered substantial attention in physics. However, the
requirement for slow evolution speed to satisfy adiabaticity greatly restricts their application …

Modern technological advances allow for the study of systems with additional synthetic
dimensions. Higher-order topological insulators in topological states of matters have been …

Thouless pump provides robust ways to realize quantized transport of waves and particles,
and it casts the static 2D quantum Hall effect onto 1D dynamic systems where one of the …