Combinatorics

Physics

T-symmetry

Brillouin zone

Geometric phase

Topology (electrical circuits)

Mathematics

Topological order

Magnetic field

Superlattice

Topological insulator

Chern class

Berry connection and curvature

Quantum Hall effect

Quantum anomalous Hall effect

Geometry

Condensed matter physics

Superconductivity

Quantum mechanics

Landau quantization

Quantum

Translational symmetry

Nature Physics

When a flat band is partially filled with electrons, strong Coulomb interactions between them may lead to the emergence of topological gapped states with quantized Hall conductivity. Such emergent topological states have been found in partially filled Landau levels1 and Hofstadter bands2,3; however, in both cases, a large magnetic field is required to produce the underlying flat band. The recent observation of quantum anomalous Hall effects in narrow-band moiré materials4–7 has led to the theoretical prediction that such phases could be realized at zero magnetic field8–12. Here we report the observation of insulators with Chern number C = 1 in the zero-magnetic-field limit at half-integer filling of the moiré superlattice unit cell in twisted monolayer–bilayer graphene7,13–15. Chern insulators in a half-filled band suggest the spontaneous doubling of the superlattice unit cell2,3,16, and our calculations find a ground state of the topological charge density wave at half-filling of the underlying band. The discovery of these topological phases at fractional superlattice filling enables the further pursuit of zero-magnetic-field phases that have fractional statistics that exist either as elementary excitations or bound to lattice dislocations. Topological states that are created from strong electron–electron interactions at half-integer superlattice fillings are observed at zero magnetic field.

Topological charge density waves at half-integer filling of a moiré superlattice