Magic-angle twisted bilayer graphene (TBG) has attracted significant interest recently due to the discoveries of diverse correlated and topological states. In this work, we study the phonon properties in magic-angle TBG based on many-body classical potential and interatomic forces generated by a deep neural network trained with data from ab initio calculations. We have discovered a number of soft modes which can exhibit dipolar, quadrupolar, and octupolar vibrational patterns in real space, as well as some time-reversal breaking chiral phonon modes. We have further studied the phonon effects on the electronic structures by freezing certain soft phonon modes. We find that if a soft quadrupolar phonon mode is assumed to be frozen, the system would exhibit a charge order which is perfectly consistent with recent experiments. Moreover, once some lowfrequency C 2z -breaking modes get frozen, the Dirac points at the charge neutrality point would be gapped out, which provides an alternative perspective to the origin of correlated insulator state at charge neutrality point.
Recently the alternating twisted trilayer graphene is discovered to exhibit unconventional superconductivity, which motivates us to study the electronic structures and possible correlation effects for this class of alternating twisted multilayer graphene (ATMG) systems. In this work we consider generic ATMG systems with M-L-N stacking configurations, in which the M (L) graphene layers and the L (N) layers are twisted by an angle θ (−θ). Based on analysis from a simplified k⋅p model approach, we derive generic partition rules for the low-energy electronic structures, which exhibit various band dispersions including two pairs of flat bands and flat bands co-existing with various gapless Fermionic excitations. For a mirror-symmetric ATMG system with doubled flat bands, we further find that Coulomb interactions may drive the system into a state with intertwined electric polarization and orbital magnetization orders, which can exhibit an interaction-driven orbital magnetoelectric effect.
In this review, we discuss the electronic structures, topological properties, correlated states, nonlinear optical responses, as well as phonon and electron-phonon coupling effects of moiré graphene superlattices. First, we illustrate that topologically non-trivial flat bands and moiré orbital magnetism are ubiquitous in various twisted graphene systems. In particular, the topological flat bands of magic-angle twisted bilayer graphene (TBG) can be explained from a zeroth pseudo-Landau-level picture, which can naturally explain the experimentally observed quantum anomalous Hall effect and some of the other correlated states. These topologically nontrivial flat bands may lead to nearly quantized piezoelectric response, which can be used to directly probe the valley Chern numbers in these moiré graphene systems. A simple and general chiral decomposition rule is reviewed and discussed, which can be used to predict the low-energy band dispersions of generic twisted mulilayer graphene system and alternating twisted multilayer graphene system. This review further discusses nontrivial interaction effects of magic-angle TBG such as the correlated insulator states, density wave states, cascade transitions, and nematic states, and proposes nonlinear optical measurement as an experimental probe to distinguish the different "featureless" correlated states.The phonon properties and electron-phonon coupling effects are also briefly reviewed. The novel physics emerging from band-aligned graphene-insulator heterostructres is also discussed in this review. In the end, we make a summary and an outlook about the novel physical properties of moiré superlattices, two-dimensional materials, moiré superlattices- two dimensional materials.
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