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

Since the discovery of topological insulators, many topological phases have been predicted
and realized in a range of different systems, providing both fascinating physics and exciting …

We present a simple prescription to flatten isolated Bloch bands with a nonzero Chern
number. We first show that approximate flattening of bands with a nonzero Chern number is …

Flatbands appear in many condensed matter systems, including the two-dimensional
electron gas in a high magnetic field, correlated materials, and moiré heterostructures. They …

We show that pressure applied to twisted WSe 2 can enhance the many-body gap and
region of stability of a fractional Chern insulator at filling ν= 1/3. Our results are based on …

The intriguing many-body phases of quantum matter arise from the interplay of particle
interactions, spatial symmetries, and external fields. Generating these phases in an …

From studies of exotic quantum many-body phenomena to applications in spintronics and
quantum information processing, topological materials are poised to revolutionize the …

Topological insulators and their intriguing edge states can be understood in a single-particle
picture and can as such be exhaustively classified. Interactions significantly complicate this …

We present a pedagogical review of the physics of fractional Chern insulators with a
particular focus on the connection to the fractional quantum Hall effect. While the latter …

We propose models of twisted multilayer graphene that exhibit exactly flat Bloch bands with
arbitrary Chern numbers and ideal band geometries. The models are constructed by twisting …