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

TL;DR

This paper investigates higher-order van Hove singularities in mirror-symmetric twisted trilayer graphene, revealing a protected zero-energy singularity with tunable properties and a topological Lifshitz transition influenced by external parameters.

Contribution

It identifies a novel higher-order van Hove singularity in twisted trilayer graphene, protected by symmetries, and explores its tunability and associated topological transition.

Findings

Discovery of a zero-energy higher-order van Hove singularity with exponent -1/3.

Identification of a topological Lifshitz transition with exponent -2/5.

Demonstration of tunability via twist angle and electric field.

Abstract

We study the presence of higher-order van Hove singularities in mirror-symmetric twisted trilayer graphene. This geometry has recently emerged experimentally as a fascinating playground for studying correlated and exotic superconducting phases. We find that the trilayer hosts a zero-energy higher-order van Hove singularity with an exponent -1/3. The singularity is protected by the threefold rotation symmetry and a combined mirror-particle-hole symmetry and it 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, beyond the recent classifications of van Hove singularities. Moreover, we find that varying a third parameter such as corrugation brings the system to a topological Lifshitz transition, with anomalous exponent -2/5, separating regions of locally open and closed semiclassical orbits.