Highero-order Van Hove singularity and Moire' of Moire' periodicity in Twisted Trilayer Graphene*

Moiré potentials obtained in twisted graphene multi-layer structures have proven remarkably fruitful for tuning the single-particle spectrum and thereby achieving exotic phases driven by the combined effects of correlation and topology. A new appealing direction has been recently opened with experiments on mirror-symmetric twisted trilayer graphene (mTTG) where only the intercalated layer is rotated by a small angle. Convincing signatures of correlated phases and superconductivity have been observed [1,2], tunable with a perpendicular electrical (displacement) field. In the first part of this talk we will argue that the single particle spectrum of mTTG shows an higher-order VHS [3] upon tuning the displacement field and rotation angle. The strong singularity is protected by the threefold rotation symmetry and a combined mirror-particle-hole symmetry. Our findings include an interesting topological Lifshitz transition when varying a third parameter, separating regions of locally open and closed semiclassical orbits. In the second part we will present a novel theory [4] for treating a different configuration of trilayer graphene, where the layers are twisted with two consecutive and independent angles. The superposition of the two different Moiré patterns gives rise to a new Moiré of Moiré periodicity on a length scale much larger than the Moiré one. Thanks to the separation between the two length scales we derive a low-energy continuum model in the Moiré of Moiré superlattice. Further, we will show that the spectrum exhibits VHS singularities at low-energy which are likely to be the precursor of strongly correlated phases [5].

[1] J.M.Park et al., Nature 590, 249–255 (2021)

[2] Z.Hao et al., Science 371, 1133–1138 (2021)

[3] D.Guerci, P.Simon, and C.Mora arXiv:2106.14911 (2021)  

[4] Y.Mao, D.Guerci, and C.Mora in preparation

[5] X.Zhang et al., PRL 127, 166802 (2021)