Laboratoire de Physique Théorique
Toulouse - UMR 5152

The experimental and theoretical success in twisted bilayer graphene (TBG) opened a new domain in modern condensed physics, now called "twistronics". Such 2D vdW heterostructures offer various platforms for the study of strongly correlated materials and hopefully topologically protected high-temperature superconductivity, paving the way to topological quantum computation and information in the future. Equipped with overly rich symmetries, different quantum topologies also emerge in such systems. A close cousin to TBG is the twisted trilayer graphene (TTG). With only an additional graphene layer, TTG exhibits significantly different properties than TBG, with even higher tunability as well as distinct symmetries and topologies. We are especially interested in the helical twisted trilayer graphene (hTTG) where the top and bottom layers are rotated in opposite directions with respect to the middle layer. In this case, two moiré patterns between neighboring layers coexist and are in general incommensurate. Therefore, the mismatch between the two moiré periodicities gives rise to a higher-level moiré pattern on top of the moiré patterns, referred to as the "moiré-of-moiré" or "supermoiré" pattern. With proper approximations, we can ignore the supermoiré variations and access the electronic state at moiré scale. Interesting topological phase transition associated with the variation of twist angle and the stacking is identified. To evaluate the supermoiré states, a theoretical framework is devised to treat it in the context of perturbed periodicity. This framework is quite general and can be applied to other physical systems. The supermoiré states can be obtained for certain twisted angles close to rational ratios. A pseudo-magnetic field effect due to the supermoiré modulation is revealed, which is otherwise invisible by the trivial average of moiré properties over the supermoiré length scale.

References :

[1] Y. Mao, D. Guerci, and C. Mora, Supermoiré low-energy effective theory of twisted trilayer graphene, Phys. Rev. B 107, 125423 (2023).

[2] D. Guerci, Y. Mao, and C. Mora, Chern mosaic and ideal flat bands in equal-twist trilayer graphene, Phys. Rev. Research 6, L022025 (2024).

[3] D. Guerci, Y. Mao, and C. Mora, Nature of even and odd magic angles in helical twisted trilayer graphene, Phys. Rev. B 109, 205411 (2024).