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 …

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 …

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 …

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

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 …

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 …

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 …

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-
plane transverse conductance becomes quantized; this is known as the quantum Hall effect …