Spectral line

Quantum mechanics

Fermi level

Magnetic field

Van Hove singularity

Graphene

Gravitational singularity

Singularity

Magic angle

Physics

Bilayer graphene

Mathematics

Topological insulator

Chern class

Condensed matter physics

Geometry

Combinatorics

Quantum Hall effect

Electron

Topology (electrical circuits)

Landau quantization

Nature Materials

Magic-angle twisted bilayer graphene exhibits intriguing quantum phase transitions triggered by enhanced electron–electron interactions when its flat bands are partially filled. However, the phases themselves and their connection to the putative non-trivial topology of the flat bands are largely unexplored. Here we report transport measurements revealing a succession of doping-induced Lifshitz transitions that are accompanied by van Hove singularities, which facilitate the emergence of correlation-induced gaps and topologically non-trivial subbands. In the presence of a magnetic field, well-quantized Hall plateaus at a filling of 1,2,3 carriers per moiré cell reveal the subband topology and signal the emergence of Chern insulators with Chern numbers, C = 3,2,1, respectively. Surprisingly, for magnetic fields exceeding 5 T we observe a van Hove singularity at a filling of 3.5, suggesting the possibility of a fractional Chern insulator. This van Hove singularity is accompanied by a crossover from low-temperature metallic, to high-temperature insulating behaviour, characteristic of entropically driven Pomeranchuk-like transitions. A magneto-transport study of twisted bilayer graphene near the magic angle further reveals its rich physics.

Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene