Supermoiré low-energy effective theory of twisted trilayer graphene

Magic-angle helical trilayer graphene

“…We propose "helical trilayer graphene" (HTG), a helical structure featuring identical rotation angles between three consecutive layers of graphene, as a promising and experimentally accessible platform for realizing exotic topological states of matter. As we will elaborate, unrelaxed HTG does not realize a single periodic moiré superlattice but instead realizes a supermoiré (or "moiré-of-moiré") structure (27)(28)(29). Nevertheless, we show that HTG locally relaxes into large regions hosting a single-moiré structure featuring a periodic honeycomb lattice of the AA stacking regions (shown in Fig.…”

Magic Angles In Equal-Twist Trilayer Graphene

“…In this letter, we focus on twisted trilayer graphene with equal small consecutive twist angles θ. We refer to such a system as equal-twist trilayer graphene (eTTG), and it is schematically represented in Fig 1 . This particular twist configuration of TTG has already been discussed in [34,[37][38][39][40].…”

“…The investigation of multiple graphene layer configurations, such as twisted trilayer graphene, is a natural generalization of the study of twisted bilayer graphene [33][34][35][36][37][38][39][40]. The multilayer systems possess greater number of parameters, which enhance their tunability.…”

“…by the lattice vectors a 1,2 = (4π/3k θ )(± √ 3/2, 1/2), with k θ = 2k D sin(θ/2), and we neglect the effects of moiré of moiré lattice [37]. It is useful to introduce complex coordinates z, z = r x ± ir y in real space and k, k = k 1 ± ik 2 in momentum space.…”

Moiré Synergy: An Emerging Playground by Coupled Moirés

“…These strong correlation effects in coupled-moiré systems share basic temperature and magnetic responses as those in single moirés, yet containing complexity and more controllable degrees of freedom. We have to admit that the field of synergetic moirés is still lacking in a general theoretic model accounting for the moiré–moiré interactions to guide the rational heterostructure design and the quantum phase discovery at this early stage, but some plausible specialized efforts have been noticed. ,, …”