Flat Chern band in a two-dimensional organometallic framework.

By combining exotic band dispersion with nontrivial band topology, an interesting type of band structure, namely, the flat Chern band, has recently been proposed to spawn high-temperature fractional quantum Hall states. Despite the proposal of several theoretical lattice models, however, it remains doubtful whether such a "romance of flatland" could exist in a real material. Here, we present a first-principles design of a two-dimensional indium-phenylene organometallic framework that realizes a nearly flat Chern band right around the Fermi level by combining lattice geometry, spin-orbit coupling, and ferromagnetism.

Stable nontrivial Z2 topology in ultrathin Bi (111) films: a first-principles study.

Recently, there have been intense efforts in searching for new topological insulator materials. Based on first-principles calculations, we find that all the ultrathin Bi (111) films are characterized by a nontrivial Z(2) number independent of the film thickness, without the odd-even oscillation of topological triviality as commonly perceived. The stable nontrivial Z(2) topology is retained by the concurrent band gap inversions at multiple time-reversal-invariant k points with the increasing film thickness and associated with the intermediate interbilayer coupling of the Bi film.

Braid group, gauge invariance, and topological order.

Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce automorphisms of the braid group, giving rise to a unified algebraic structure that characterizes the ground-state subspace and fractionally charged, anyonic quasiparticles. Minimal ground-state degeneracy is derived without assuming any relation between quasiparticle charge and statistics.