Stacking and gate tunable topological flat bands, gaps and anisotropic strip patterns in twisted trilayer graphene

Abstract

Trilayer graphene with a twisted middle layer has recently emerged as a new platform exhibiting correlated phases and superconductivity near its magic angle. A detailed characterization of its electronic structure in the parameter space of twist angle θ, interlayer potential difference ∆, and topbottom layer stacking τ reveals that flat bands with large Coulomb energy vs bandwidth U/W > 1 are expected within a range of ±0.2 • near θ 1.5 • and θ 1.2 • for τAA top-bottom layer stacking, between a wider 1 • ∼ 1.7 • range for τAB stacking, whose bands often have finite valley Chern numbers thanks to the opening of primary and secondary band gaps in the presence of a finite ∆, and below θ 0.6 • for all τ considered. The largest U/W ratios are expected at the magic angle ∼ 1.5 • when |∆| ∼ 0 meV for AA, and slightly below near ∼ 1.4 • for finite |∆| ∼ 25 meV for AB stackings, and near θ ∼ 0.4 • for both stackings. When τ is the saddle point stacking vector between AB and BA we observe pronounced anisotropic local density of states (LDOS) strip patterns with broken triangular rotational symmetry. We present optical conductivity calculations that reflect the changes in the electronic structure introduced by the stacking and gate tunable system parameters.

Correlated insulators, semimetals, and superconductivity in twisted trilayer graphene

“…32 finds that the superconductor can sustain an in-plane magnetic field much larger than simple estimates of the Pauli limit. One additional crucial difference between MSTG and all of the other graphene moiré systems mentioned above is that MSTG not only exhibits quasi-flat bands but, at the same time, dispersive Dirac cones [30,31,[33][34][35][36][37][38]. The interplay between these different types of bands and interactions likely gives rise to rich physics but also provides theoretical challenges.…”

Band Structure and Superconductivity in Twisted Trilayer Graphene

“…This symmetry can be broken by various experimentally-relevant perturbations. In this case, calculations of the electronic structure in the absence of this mirror symmetry shows hybridized monolayer and twisted bilayer features [3,[23][24][25][26][27]. The effect of electron-electron interactions have also been considered [24][25][26][27][28][29][30], as well as the role of external magnetic fields [31].…”

Higher-order van Hove singularity in magic-angle twisted trilayer graphene

“…[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. A new appealing direction has been recently opened with experiments on trilayer graphene [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67] where only the intercalated layer is rotated by a small angle. Convincing signatures of correlated phases and superconductivity have been observed [68,69], tunable with a perpendicular electrical (displacement) field.…”