TB or not TB? Contrasting properties of twisted bilayer graphene and the alternating twist $n$-layer structures ($n=3, 4, 5, \dots$)

Abstract

The emergence of alternating twist multilayer graphene (ATMG) as a generalization of twisted bilayer graphene (TBG) raises the question -in what important ways do these systems differ? Here, we utilize a combination of techniques including ab-initio relaxation and single-particle theory, analytical strong coupling analysis, and Hartree-Fock to contrast ATMG with n = 3, 4, 5, . . . layers and TBG. I: We show how external fields enter in the decomposition of ATMG into twisted bilayer graphene and graphene subsystems. The parallel magnetic field is expected to have a much smaller effect when n is odd due to mirror symmetry, but surprisingly also for any n > 2 if we are are the largest magic angle. II: We compute the lattice relaxation of the multilayers leading to the effective parameters for each TBG subsystem as well as small mixing between the subsystems. We find that the second magic angle for n = 5, θ ≈ 1.14, provides the closest realization of the "chiral" model and is protected from mixing by mirror symmetry. It may be an optimal host for fractional Chern insulators. III: When there are no external fields, we integrate out the non-magic subsystems and reduce ATMG to the magic angle TBG subsystem with a screened interaction. IV: We perform an analytic strong coupling analysis of the effect of external fields and corroborate our results with numerical Hartree Fock simulations. For TBG itself, we find that an in-plane magnetic field can drive a phase transition to a valley Hall state or a gapless "magnetic semimetal" while having a weaker effect on n ≥ 3 ATMG at the first magic angle. In contrast, displacement field (V ) has very little effect on TBG, but induces a gapped phase in ATMG for small V for n = 4 and above a finite critical V for n = 3. For n ≥ 3, we extract the superexchange coupling -believed to set the scale of superconductivity in the skyrmion mechanism -and show that it increases with V at angles near and below the magic angle. V: We complement our strong coupling approach with a phenomenological weak coupling theory of ATMG pair-breaking. While for n = 2 orbital effects of the in-plane magnetic field can give a critical field of the same order as the Pauli field, for n > 2 we expect the critical field to exceed the Pauli limit. Contents A. n = 2 B. n = 3 C. General n VII. Conclusions VIII. Acknowledgements References SI. Review of the mapping twisted multilayer graphene to TBG A. Trilayer n = 3 B. Tetralayer n = 4 C. n = 5 SII. Lattice relaxation A. Summary of relaxation calculation B. Effect of lattice relaxation on magic angles and the multilayer mapping SIII. Intra-TBG effects of external fields A. External fields in n = 2 MATBG 1. Electric field 2. Magnetic field B. Even n¿2

Ascendance of Superconductivity in Magic-Angle Graphene Multilayers

“…We chose w = 60 meV for all three multilayers considered, which is in agreement with the estimates of Ref. 24 and similar to values used previously for TBG/WSe 2 structures 14 .…”

“…4c inset), confirm-ing its robust nature. We emphasize that the unprecedented persistence of superconductivity across a large filling factor range in TPG (and also TQG in comparison to TTG or TBG) cannot be explained in a minimal framework of alternating twisted graphene multilayers 8,24 without invoking the non-trivial role of the additional bands.…”

Field-tuned and zero-field fractional Chern insulators in magic angle graphene

“…Initial abinitio estimates based on out-of-plane relaxation alone [55] yielded κ ≈ 0.8. Contributions from in-plane relaxation [53,54,[56][57][58][59] further reduces this value, so κ estimates vary from 0.5 − 0.8 -see for example Ref. [58] in which the values of κ vary dramatically for different choices of inter-atomic potentials and tight-binding parameterizations; such choices can be motivated by electronic screening or reduction of out-of-plane relaxation by the hBN substrate.…”

“…A recent calculation in Ref. [59] uses first principles calculations for these parameterizations [60,61] and yields κ = 0.53, although this calculation also depends on the chosen density functional. We note that STM experiments can visualize the size of AA and AB regions and has been used to estimate a value of κ around 0.8 [62].…”

Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization

“…We fix w AB = 110 meV but consider variable w AA , thereby tuning the value of the chiral ratio κ ≡ w AA /w AB . Estimated values for κ in the literature range from 0.5 to 0.8 [54][55][56] . The kinetic bandwidth is minimal when the twist angle θ is close to the magic angle, which is weakly dependent on κ.…”