Alternating twisted mutilayer graphene: generic partition rules, double flat bands, and orbital magnetoelectric effect

Abstract

Twisted graphene systems have draw significant attention due to the discoveries of various correlated and topological phases. In particular, recently the alternating twisted trilayer graphene is discovered to exhibit unconventional superconductivity, which motivates us to study the electronic structures and possible interesting correlation effects of this class of alternating twisted graphene systems. In this work we consider generic alternating twisted multilayer graphene (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 analytically derive generic partition rules for the low-energy electronic structures, which exhibit various intriguing band dispersions including one pair of flat bands, two pairs of flat bands, as well as flat bands co-existing with with Dirac cones, quadratic bands, or more generally E(k) ∼ k J dispersions (J is positive integer) for each spin and valley. Such unusual non-interacting electronic structures may have unconventional correlation effects. Especially for a mirror symmetric ATMG system with two pairs of flat bands (per spin per valley), we find that Coulomb interactions may drive the system into a state breaking both time-reversal and mirror symmetries, which can exhibit a novel type of orbital magnetoelectric effect due to the interwining of electric polarization and orbital magnetization orders in the symmetry-breaking state.

Ascendance of Superconductivity in Magic-Angle Graphene Multilayers

“…This feature distinguishes TPG and TQG structures from TTG and may therefore play a role in explaining extensive superconducting regions. Finally, we mention that other effects, such as strain 31 , or a different stacking order, may yield multiple sets of flat bands 32 (see SI, section 4b) even at the non-interacting level, in which case multiple bands can host superconductivity independently. Importantly, however, invoking this explanation would place TQG and TPG well outside a simple TBG paradigm, as coexisting but independent sets of flat TBG-like bands are expected to produce more cascade resets than observed experimentally, and therefore are unlikely.…”

Moire Band Structures of the Double twisted Few Layer Graphene

“…Note added.-Recently, we become aware of a preprint which also discuss the moiré bands of the (2+1+2)-ATFLG 73 .…”