Kekulé Spiral Order at All Nonzero Integer Fillings in Twisted Bilayer Graphene

Kwan, Yves H.; Wagner, Glenn; Soejima, Tomohiro; Zaletel, MP; Simon, SH; Parameswaran, S. A.; Bultinck, Nick

doi:10.1103/physrevx.11.041063

Cited by 78 publications

(53 citation statements)

References 128 publications

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“…We observe an unexpected anomalous Hall effect at half filling in these devices, arising from a new correlated ground state with finite orbital magnetization that is most naturally explained by the formation of a valley-polarized phase. However, valley-polarized states are generally not predicted to be favored in the strong-coupling limit at halffilling [10,[13][14][15][16], nor have they been observed at zero field in any previously reported tBLG device (except with the addition of proximity-induced spin-orbit coupling [18]). This suggests that competing symmetrybroken orders can become preferred as the interaction strength is reduced by tuning away from the magic angle, necessitating a more careful theoretical treatment of tBLG in the intermediately-coupled regime.…”

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confidence: 85%

“…In particular, the anomalous Hall effect (AHE) has been observed at odd integer filling factors (ν = 1 and 3) in a small number of tBLG devices [5,6,9], indicating the emergence of a zero-field orbital magnetic state with spontaneously broken time-reversal symmetry [10][11][12]. However, the AHE is typically not anticipated at half filling (ν = 2) owing to competing intervalley coherent states [10,[13][14][15][16], as well as spin-polarized and valley Hall states that are favored by an intervalley Hund's coupling [10,[16][17][18]. Here, we present measurements of two tBLG devices with twist angles slightly away from the magic angle (0.96 • and 1.20 • ), in which we report the surprising observation of the AHE at ν = +2 and −2, respectively.…”

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confidence: 99%

“…Such a state spontaneously breaks time-reversal symmetry, resulting in an AHE due to the large Berry curvature concentrated at the band extrema. In C 2 T -symmetric tBLG (C 2 is a two-fold rotation and T is time reversal), Hartree-Fock calculations performed in the strong-coupling limit predict either a Kramers intervalley coherent (K-IVC) or an incommensurate Kekulé spiral (IKS) order [10,[13][14][15][16], depending on the precise magnitude of heterostrain in the structure [15,16]. However, the IKS state is timereversal symmetric [15], and although the K-IVC features local magnetic moments on the moiré-scale, it is also time-reversal symmetric upon spatial averaging [13].…”

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confidence: 99%

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Anomalous Hall effect at half filling in twisted bilayer graphene

Tseng¹,

Ma²,

Liu³

et al. 2022

Preprint

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confidence: 85%

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confidence: 99%

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confidence: 99%

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Anomalous Hall effect at half filling in twisted bilayer graphene

Tseng¹,

Ma²,

Liu³

et al. 2022

Preprint

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“…The discovery of superconductivity and correlated insulators in twisted bilayer graphene (TBG) [1,2] close to the theoretically predicted magic angle θ TBG ≈ 1.1 o [3][4][5][6] has stimulated a huge amount of experimental [7][8][9][10][11][12][13][14][15][16][17] and theoretical work [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][33][34][35][36][37][38][39][40][41][42][43] on the system. In addition to the correlated insulators and superconductivity observed in the early works, more recent discoveries include the quantum anomalous Hall states with [44][45][46][47] and without…”

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confidence: 95%

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

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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

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“…29 Alternatively, 𝐶 = 0 states at both non zero fillings 𝜈 = 2, 3 are also consistent with the recently proposed time-reversal symmetric "incommensurate Kekulé spiral" (IKS) order which appears in the presence of strain. 30 Further studies are needed to uncover the competitions of these Chern insulator states in MATTG which are determined by symmetry breaking that is sensitive to specific parameters like strain and magnetic field.…”

Section: Extraction Of Chern Numbersmentioning

confidence: 99%

Dirac cone spectroscopy of strongly correlated phases in twisted trilayer graphene

Cheng

Ledwith

Watanabe

et al. 2022

Preprint

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Mirror-symmetric magic-angle twisted trilayer graphene (MATTG) hosts flat electronic bands close to zero energy, and has been recently shown to exhibit abundant correlated quantum phases with flexible electrical tunability.1–3 However studying these phases proved challenging as these are obscured by intertwined Dirac bands. In this work, we demonstrate a novel spectroscopy technique, that allows to quantify the energy gaps and Chern numbers of the correlated states in MATTG by driving band crossings between Dirac cone Landau levels and the energy gaps in the flat bands. We uncover hard correlated gaps with Chern numbers of C = 0 at integer moiré unit cell fillings of ν = 2 and 3 and reveal novel charge density wave states originating from van Hove singularities at fractional fillings of ν = 5/3 and 11/3. In addition, we demonstrate the existence of displacement field driven first-order phase transitions at charge neutrality and half fillings of the moiré unit cell ν = ± 2, which is consistent with a theoretical strong-coupling analysis, implying the breaking of the C2T symmetry. Overall these properties establish the diverse and electrically tunable phase diagram of MATTG and provide an avenue for investigating electronic quantum phases and strong correlations in multiple-band moiré systems.

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Kekulé Spiral Order at All Nonzero Integer Fillings in Twisted Bilayer Graphene

Cited by 78 publications

References 128 publications

Anomalous Hall effect at half filling in twisted bilayer graphene

Anomalous Hall effect at half filling in twisted bilayer graphene

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

Dirac cone spectroscopy of strongly correlated phases in twisted trilayer graphene

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