The past decade has witnessed remarkable experimental achievements in the study of graphene and related two-dimensional materials. Stacking monolayers of graphene with a small twist angle forming moiré patterns has been demonstrated to dramatically change the band structure, generating gaps and band flattening. The discovery in 2018 of correlated insulating phases and superconductivity [1] in twisted bilayer graphene has given a very strong boost to the field. It clearly offers a versatile platform to explore strongly correlated matter in a relatively simple system.
Even more recently, similar correlated insulating phases have been observed with three twisted layers of graphene [2], together with a more abundant superconducting phase. After a general introduction to the physics of twisted bilayer and trilayer graphene systems, I will discuss the emergence of van Hove singularities in mirror-symmetric twisted trilayer graphene. Our findings [3] include a zero-energy higher-order van Hove singularity protected by the threefold rotation symmetry and a combined mirror-particle-hole symmetry. It is tuned by varying the twist angle and a perpendicular electric field by gating. Such strong van Hove singularity is likely to be the precursor of strongly correlated phases. In addition, we find an interesting topological Lifshitz transition when varying a third parameter, separating regions of locally open and closed semiclassical orbits.
[1] Y. Cao et al., Nature 556, 43 (2018); Y. Cao et al., Nature 556, 80 (2018).
[2] J.M. Park et al., Nature 590, 249–255 (2021).
[3] D. Guerci, P. Simon and C. Mora, arXiv:2106.14911
