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

Certain lattice wave systems in translationally invariant settings have one or more spectral
bands that are strictly flat or independent of momentum in the tight binding approximation …

Time-periodic forcing in the form of coherent radiation is a standard tool for the coherent
manipulation of small quantum systems like single atoms. In the last years, periodic driving …

While regular flat bands are good for enhancing the density of states and hence the gap,
they are detrimental to the superfluid weight. We show that the predicted nontrivial topology …

Topological invariants built from the periodic Bloch functions characterize new phases of
matter, such as topological insulators and topological superconductors. The most important …

Exotic phases of matter can emerge from the interplay between strong electron interactions
and non-trivial topology. Materials that have non-dispersing bands in their electronic band …

Two-dimensional lattices of coupled micropillars etched in a planar semiconductor
microcavity offer a workbench to engineer the band structure of polaritons. We report …

The ground state and transport properties of the Lieb lattice flat band in the presence of an
attractive Hubbard interaction are considered. It is shown that the superfluid weight can be …

Although kinetic energy of a massive particle generally has quadratic dependence on its
momentum, a flat, dispersionless energy band is realized in crystals with specific lattice …

We report on the engineering of a nondispersive (flat) energy band in a geometrically
frustrated lattice of micropillar optical cavities. By taking advantage of the non-Hermitian …