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

Guerci, Daniele; Simon, Pascal; Mora, Christophe

doi:10.1103/physrevresearch.4.l012013

Cited by 28 publications

(8 citation statements)

References 88 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This makes them promising platforms to realize all the phases seen in TBG including superconductivity, if the symmetry ingredients have been correctly identified. Twisted trilayer graphene (TTG) is therefore a natural next step after twisted bilayer both experimentally [73][74][75][76][77] and theoretically [78][79][80][81][82][83][84][85][86][87]. It is a structure that is symmetric under mirror symmetry M z and it decomposes into twisted bilayer graphene and ordinary graphene where the subsystems are in opposite mirror sectors [88].…”

mentioning

confidence: 99%

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

Ledwith¹,

Khalaf²,

Zhu³

et al. 2021

Preprint

View full text Add to dashboard Cite

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

show abstract

mentioning

confidence: 99%

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

Ledwith¹,

Khalaf²,

Zhu³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…These multilayer systems offer increased tunability due to a larger set of parameters [KKAJ19,LVK22]. We also want to mention recent progress on a helical version of twisted trilayer graphene [Dev23,GMM23a,GMM23b]. The study of the continuum or Bistritzer-MacDonald (BM) model for twisted trilayer graphene exhibits, unlike the BM model for bilayer graphene [BM11], commensurable and incommensurable twisting angles (see Assumption 1).…”

Section: Introductionmentioning

confidence: 99%

Mathematics of magic angles in a model of twisted bilayer graphene

et al. 2022

View full text Add to dashboard Cite

We study Dirac points of the chiral model of twisted bilayer graphene (TBG) with constant in-plane magnetic field. For a fixed small magnetic field, we show that as the angle of twisting varies between magic angles, the Dirac points move between K, K points and the Γ point. The Dirac points for zero magnetic field and non magic angles lie at K and K , while in the presence of a non-zero magnetic field and near magic angles, they lie near the Γ point. For special directions of the magnetic field, we show that the Dirac points move, as the twisting angle varies, along straight lines and bifurcate orthogonally at distinguished points. At the bifurcation points, the linear dispersion relation of the merging Dirac points disappears and exhibit a quadratic band crossing point (QBCP). The results are illustrated by links to animations suggesting interesting additional structure.

show abstract

“…Besides the conventional van Hove singularity (CVHS), the moiré system also allows for feasible realizations of the higher order van Hove singularity (HOVHS) [32][33][34]. Using the notations above, a HOVHS can be formally defined as the case when det D = 0.…”

Section: Introductionmentioning

confidence: 99%

Pair density wave and loop current promoted by van Hove singularities in moiré systems

Wu¹,

Wu²,

Wu³

2022

Preprint

View full text Add to dashboard Cite

We theoretically show that in the presence of conventional or higher order van Hove singularities(VHS), the bare finite momentum pairing, also known as the pair density wave (PDW), susceptibility can be promoted to the same order of the most divergent bare BCS susceptibility through a valley-contrasting flux 3φ in each triangular plaquette at φ = π 3 and φ = π 6 in moiré systems. This makes the PDW order a possible leading instability for an electronic system with repulsive interactions. We confirm that it indeed wins over all other instabilities and becomes the ground state under certain conditions through the renormalization group calculation and a flux insertion argument. Moreover, we also find that a topological nontrivial loop current order becomes the leading instability if the Fermi surface with conventional VHS is perfectly nested at φ = π 3 . Similar to the Haldane model, this loop current state has the quantum anomalous Hall effect. If we dope this loop current state or introduce a finite next-nearest neighbour hopping t , the chiral d-wave PDW becomes the dominant instability. Experimentally, the flux can be effectively tuned by an out-of-plane electric field in moiré systems based on graphene and transition metal dichalcogenides.

show abstract

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

Cited by 28 publications

References 88 publications

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

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

Mathematics of magic angles in a model of twisted bilayer graphene

Pair density wave and loop current promoted by van Hove singularities in moiré systems

Contact Info

Product

Resources

About