Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands

Kang, Jian; Vafek, Oskar

doi:10.1103/physrevlett.122.246401

Cited by 357 publications

(363 citation statements)

References 37 publications

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“…The emergence of magnetism in this flat-band angle regime is analogous to observations of magnetic instabilities at other angles and dopings [37,38], in particular, in magic-angle superlattices [51][52][53]. Unique to our regime is the sensitivity of the ±1-pLL bands to an interlayer voltage-bias: as elaborated below, the latter modifies the electronic spectrum of the bilayer and hence allows for the tuning of the aforementioned magnetic order.…”

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confidence: 62%

Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene

et al. 2019

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Twisted graphene bilayers provide a versatile platform to engineer metamaterials with novel emergent properties by exploiting the resulting geometric moiré superlattice. Such superlattices are known to host bulk valley currents at tiny angles (α ≈ 0.3 • ) and flat bands at magic angles (α ≈ 1 • ). We show that tuning the twist angle to α * ≈ 0.8 • generates flat bands with triangular superlattice periodicity. When doped with ±6 electrons per moiré cell, these bands are half-filled and electronic interactions produce a symmetry-broken ground state (Stoner instability) with spin-polarized regions that order ferromagnetically. Application of an interlayer electric field breaks inversion symmetry and introduces valley-dependent dispersion that quenches the magnetic order. With these results, we propose a solid-state platform that realizes electrically tunable strong correlations. arXiv:1905.07651v3 [cond-mat.mes-hall]

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confidence: 62%

Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene

et al. 2019

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“…The possibility of magnetic order in magic-angle tBLG was also previously discussed in Refs. [26,[57][58][59][60][61][62][63][64].…”

Section: Su(2)+×su(2)− Symmetry Breaking Effectsmentioning

confidence: 99%

Symmetry breaking and skyrmionic transport in twisted bilayer graphene

2020

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Motivated by recent low-temperature magnetoresistance measurements in twisted bilayer graphene aligned with hexagonal Boron Nitride substrate, we perform a systematic study of possible symmetry breaking orders in this device at a filling of two electrons per Moiré unit cell. We find that the surprising non-monotonic dependence of the resistance on an out-of-plane magnetic field is difficult to reconcile with particle-hole charge carriers from the low-energy bands in symmetry broken phases. We invoke the non-zero Chern numbers of the twisted bilayer graphene flat bands to argue that skyrmion textures provide an alternative for the dominant charge carriers. Via an effective field-theory for the spin degrees of freedom, we show that the effect of spin Zeeman splitting on the skyrmion excitations provides a possible explanation for the non-monotonic magnetoresistance. We suggest several experimental tests, including the functional dependence of the activation gap on the magnetic field, for our proposed correlated insulating states at different integer fillings. We also discuss possible exotic phases and quantum phase transitions that can arise via skyrmion-pairing on doping such an insulator. arXiv:1908.00986v1 [cond-mat.str-el]

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“…The possibility of spin and valley polarization and/or quantum anomalous Hall physics and chiral edge states in TBG has been discussed previously in Refs. [43][44][45][46][47][48][49][50][51], albeit from a different perspective. In particular, Ref.…”

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Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene

2020

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We use a lowest Landau level model to study the recent observation of an anomalous Hall effect in twisted bilayer graphene. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structure of the flat bands precludes an instability to an inter-valley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.Moiré graphene systems are a class of simple van der Waals heterostructures [1] hosting interaction driven lowenergy physics, making them an exciting platform to advance our understanding of strongly correlated quantum matter. In twisted bilayer graphene (TBG) with a small twist angle between adjacent layers, interaction effects are enhanced by van Hove singularities coming from 8 bands around charge neutrality in the Moiré-or mini-Brillouin zone (mBZ) with a very small bandwidth [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. A confirmation of the important role played by interactions in these mBZ flat bands was provided in Ref. [22] and Refs. [23][24][25][26][27], where interaction-dominated gaps were observed when 2 or 6 (filling ν = −2, 2) of the 8 flat bands in TBG are filled. Also in ABC stacked trilayer graphene Moiré systems Mott insulating behavior has been reported [28]. Interestingly, at densities near some of these Mott insulators the system becomes superconducting [25,29].Recent experiments indicate that certain magic angle graphene devices have large resistance peaks at ν = 0, 3, with the latter featuring an anomalous Hall (AH) effect detected via hysteresis in the Hall conductance as a function of the out-of-plane magnetic field [30]. The Hall conductance is of order e 2 /h but not yet quantized. Some have detected an meV-scale gap at charge neutrality, and a hysteretic behaviour of the Hall conductance with applied field at ν = −1 [31]. In this work we discuss how the breaking of the 180-degree rotational symmetry (C 2z ) by a partially aligned hexagonal boron-nitride (h-BN) substrate could explain these observations. A variety of works [32][33][34][35][36][37][38] have found that h-BN opens up a band gap at the Dirac points of monolayer graphene whose magnitude depends on the graphene / h-BN alignment angle, reaching ∆ AB ∼ 17meV [38] to ∼ 30meV [36, 37] at perfect alignment. Notably, even in seemingly unaligned devices with little or no observable h-BN induced Moiré potential, band gaps of several meV are still observed [37,38]. In TBG, the substrate can likewise gap-out the flat band Dirac points at the K ± points of the mBZ, splitting the bands as 8 = 4 + 4 to create a gap at charge * N.B. and S.C. contributed equally to this w...

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Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands

Cited by 357 publications

References 37 publications

Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene

Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene

Symmetry breaking and skyrmionic transport in twisted bilayer graphene

Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene

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