Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the… Expand

It is shown, both theoretically and experimentally, that one-dimensional quasicrystals are assigned two-dimensional Chern numbers and, respectively, exhibit topologically protected boundary states equivalent to the edge states of a two- dimensional quantum Hall system.Expand

This work describes in detail how this daubechies wavelets basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations.Expand

Thouless introduced the idea of a topological charge pump: the quantized motion of charge due to the slow cyclic variation of a periodic potential. This topologically protected transport has now been… Expand

This work explores the influence of dissipation on a paradigmatic driven-dissipative model where a collection of two level atoms interact with both quadratures of a quantum cavity mode and shows that, surprisingly, the tricritical points exhibit anomalous finite fluctuations, as opposed to standard trICritical points arising in ^{3}He-^{4}He mixtures.Expand

It is shown that a previously inaccessible phase of matter-the 4D integer quantum Hall effect-can be incorporated in a 2D quasicrystal, and may pave the way to the experimental study of 4D physics.Expand

These findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.Expand

This work uses tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally, and provides a platform for the study of higher-dimensional topological physics.Expand

This work identifies the linear and nonlinear quantized current responses of the 4D model, relating these to the topology of the Bloch bands, and proposes experimental protocols, based on current or center-of-mass-drift measurements, to extract the topological second Chern number.Expand

This work shows that it is feasible to generate and control highly indistinguishable single-photon topological states, opening pathways to enhanced photonic quantum technology with topological properties, and to study quantum effects in topological materials.Expand