Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene

Abstract

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...

Giant orbital magnetoelectric effect and current-induced magnetization switching in twisted bilayer graphene

“…For isolated TBG, the point group symmetry is D 6 which allows a longitudinal response only, so the induced magnetization will be parallel to the direction of the current as shown in Table I. However, the substrate can strongly affect the properties of TBGs [26][27][28][29]. Effects of a rotationally-aligned hBN substrate on the nearest graphene layer are to break the sublattice symmetry and to induce strain so that the symmetry of the full TBG stack is reduced to C 1 .…”

Symmetry breaking and skyrmionic transport in twisted bilayer graphene

“…In Refs. [27,28], it was found that a non-zero sublattice splitting on one side of magic-angle tBLG gaps out all Dirac cones of the Moiré Hamiltonian. Because the two Dirac cones in a single-valley Moiré Hamiltonian, shown in Fig.…”

“…For instance in tBLG, the flat bands have non-trivial fragile topology protected by the space group symmetries [21][22][23][24]. In devices which have isolated flat bands, one generally finds broad parameter regimes where these bands have non-zero Chern number [19,20,[25][26][27][28].…”

Particle-Hole Duality, Emergent Fermi Liquids, and Fractional Chern Insulators in Moiré Flatbands

“…Most saliently, we provide microscopic evidence that high temperature fractional Chern insulators can form in twisted bilayer graphene aligned with hexagonal boron nitride.Setup. Motived by the recent discoveries [11][12][13]15] along with theoretical predictions [16,21] of spin and valley polarized insulators at integer fillings in various Moiré bands, we consider electrons with polarized spin arXiv:1912.04907v1 [cond-mat.mes-hall]…”