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 …

Electronic states in quasicrystals generally preclude a Bloch description, rendering them
fascinating and enigmatic. Owing to their complexity and scarcity, quasicrystals are …

While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in
controlling dissipation have brought about unprecedented flexibility in engineering non …

There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …

In the field of quantum simulation of condensed matter phenomena by artificially
engineering the Hamiltonian of an atomic, molecular or optical system, the concept of …

Thouless pum** enables topological transport and the direct measurement of topological
invariants. So far, realizations of Thouless pum** rely on the adiabatic evolution of a …

A non-Hermitian system can exhibit extensive sensitivity of its complex energy spectrum to
the imposed boundary conditions, which is beyond any known phenomenon from Hermitian …

Topological band theory establishes a standardized framework for classifying different types
of topological matters. Recent investigations have shown that hyperbolic lattices in non …

The physics of a photonic structure is commonly described in terms of its apparent geometric
dimensionality. On the other hand, with the concept of synthetic dimension, it is in fact …