Higher-order Van Hove singularity in magic-angle twisted trilayer graphene

Twisted trilayer graphene (TTG) has recently emerged experimentally as a fascinating playground to study correlated and exotic superconducting phases. We have found that TTG hosts a zero-energy higher-order Van Hove singularity with an exponent −1/3 that is stronger than the one predicted in twisted bilayer graphene. This singularity is protected by a threefold rotation symmetry and a combined mirror-particle-hole symmetry and can be tuned with only the twist angle and a perpendicular electric field. It arises from the combined merging of Van Hove singularities and Dirac cones at zero energy, a scheme that goes beyond the recent classifications of Van Hove singularities in single-band models. This structure gives a topological Lifshitz transition, with anomalous exponent −2/5, which can be achieved in TTG by varying a third control parameter such as the atomic corrugation. The interplay between the nonstandard class of higher-order Van Hove singularities and interaction effects offers an unprecedented platform for studying correlation and superconductivity