The quantum anomalous Hall effect (QAHE) is a fundamental transport phenomenon in the field of condensed-matter physics. Without an external magnetic field, spontaneous magnetization combined with spin-orbit coupling gives rise to a quantized Hall conductivity. So far, a number of theoretical proposals have been made to realize the QAHE, but all based on inorganic materials. Here, using first-principles calculations, we predict a family of 2D organic topological insulators for realizing the QAHE. Designed by assembling molecular building blocks of triphenyl-transition-metal compounds into a hexagonal lattice, this new class of organic materials is shown to have a nonzero Chern number and exhibits a gapless chiral edge state within the Dirac gap.

By combining scanning tunneling microscopy and spectroscopy, angle-resolved photoemission spectroscopy, and density functional theory band calculations, we directly observe and resolve the one-dimensional edge states of single bilayer (BL) Bi(111) islands on clean ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and Bi(111)-covered ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ substrates. The edge states are localized in the vicinity of step edges having an $\sim 2\mathrm{nm}$ wide spatial distribution in real space and reside in the energy gap of the Bi(111) BL. Our results demonstrate the existence of nontrivial topological edge states of single Bi(111) bilayer as a two-dimensional topological insulator.

Topological insulators are a recently discovered class of materials having insulating bulk electronic states but conducting boundary states distinguished by nontrivial topology. So far, several generations of topological insulators have been theoretically predicted and experimentally confirmed, all based on inorganic materials. Here, based on first-principles calculations, we predict a family of two-dimensional organic topological insulators made of organometallic lattices. Designed by assembling molecular building blocks of triphenyl-metal compounds with strong spin-orbit coupling into a hexagonal lattice, this new classes of organic topological insulators are shown to exhibit nontrivial topological edge states that are robust against significant lattice strain. We envision that organic topological insulators will greatly broaden the scientific and technological impact of topological insulators.

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. An effective four-band model is constructed to reproduce the first-principles results. Our design, in addition, provides a general strategy to synthesize topologically nontrivial materials by virtue of organic chemistry and nanotechnology.