Energetic stability and spatial inhomogeneity in the local electronic structure of relaxed twisted trilayer graphene

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.…”

Intrinsically-multilayer moiré heterostructures

“…In other words, an intrinsically n-layer moiré material is one whose singular configuration is a sum of reciprocal lattice vectors from all layers that add to zero, but no two vectors from that sum add to zero by themselves. Notice this is distinct from, e.g., helicallytwisted trilayer graphene [53][54][55][56]; there the singular pattern is at zero twist angle, where any two layers have reciprocal lattice vectors which add to zero. (Patterns where some layers are aligned, such as alternating-twisted trilayer [46,47] and twisted double bilayer graphene [48][49][50][51], often have patterns that arise from only two misaligned sets of layers, rather than more than two; moreover, such patterns are always singular in themselves.)…”

“…The observation of superconductivity and correlated insulators in twisted bilayer graphene [1,2] launched the study of "moiré materials," where two-dimensional materials with the same or similar [36][37][38][39][40][41][42][43][44][45] lattice constants are stacked at a small relative twist angle. This paradigm is naturally extended to trilayer stacking and beyond, both with some layers aligned [46][47][48][49][50][51][52] and with multiple twist angles [53][54][55][56][57][58]. Recently it has also been extended to stacking at angles nearby a large commensurate twist angle [59,60].…”

Pseudomagnetic fields in fully relaxed twisted bilayer and trilayer graphene

“…Lattice relaxation has been shown to play a pivotal role in the piezoelectric, ferroelectric and electronic properties of twisted TMDs [26][27][28][29][30][31][32][33][34][35][36][37][38][39] as well as in the charge density wave phases of twisted NbSe 2 [40,41]. In graphitic systems [42], atomic relaxation has been shown to determine the outof-plane polarization of twin boundaries [43] while in supermoiré systems such as the non-symmetric twisted trilayer graphene, lattice relaxation leads to a clear separation between the flat band and the highly dispersive Dirac cone [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. For sufficiently small twist angles, θ ≲ 0.5 • , a domain pattern, made of AB and BA regions separated by domain walls emerges, leading to a conducting network of topologically protected 1D channels [61][62][63][64][65][66].…”