Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems

Abstract

We study the electronic structures and topological properties of $(M+N)$-layer twisted graphene systems. We consider the generic situation that $N$-layer graphene is placed on top of the other $M$-layer graphene, and is twisted with respect to each other by an angle $\theta$. In such twisted multilayer graphene (TMG) systems, we find that there exists two low-energy flat bands for each valley emerging from the interface between the $M$ layers and the $N$ layers. These two low-energy bands in the TMG system possess valley Chern numbers that are dependent on both the number of layers and the stacking chiralities. In particular, when the stacking chiralities of the $M$ layers and $N$ layers are opposite, the total Chern number of the two low-energy bands for each valley equals to $\pm (M+N-2)$ (per spin). If the stacking chiralities of the $M$ layers and the $N$ layers are the same, then the total Chern number of the two low-energy bands for each valley is $\pm (M-N)$ (per spin). The valley Chern numbers of the low-energy bands are associated with large, valley-contrasting orbital magnetizations, suggesting the possible existence of orbital ferromagnetism and anomalous Hall effect once the valley degeneracy is lifted either externally by a weak magnetic field or internally by Coulomb interaction through spontaneous symmetry breaking.

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Cited by in corpus (144)

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• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Ferromagnetism in narrow bands of moiré superlattices
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides
• Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
• Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene
• Moiré Flat Bands in Twisted Double Bilayer Graphene
• Atypical sliding and Moire ferroelectricity in pure multilayer graphene
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• Electronic band structure and pinning of Fermi energy to van Hove singularities in twisted bilayer graphene: a self consistent approach
• Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a $k\cdot p$ 2-Band model
• Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene
• Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Symmetry breaking and skyrmionic transport in twisted bilayer graphene
• Emulating heavy fermions in twisted trilayer graphene
• Magic-angle helical trilayer graphene
• Topological flat bands in twisted trilayer graphene
• Heavy fermion representation for twisted bilayer graphene systems
• Experimental evidence for orbital magnetic moments generated by moiré-scale current loops in twisted bilayer graphene
• Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory
• A perspective of twisted photonic structures
• Gap Opening in Twisted Double Bilayer Graphene by Crystal fields
• Anomalous Hall effect, magneto-optical properties, and nonlinear optical properties of twisted graphene systems
• Mirror Symmetry Breaking and Lateral Stacking Shifts in Twisted Trilayer Graphene
• Gate tunable topological flat bands in twisted monolayer-bilayer graphene
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Nonlinear anomalous Hall effects probe topological phase-transitions in twisted double bilayer graphene
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Higher-order van Hove singularity in magic-angle twisted trilayer graphene
• Ferromagnetism and superconductivity in twisted double bilayer graphene
• Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene
• Pairing in graphene-based moiré superlattices
• Dynamical correlations and order in magic-angle twisted bilayer graphene
• Isospin competitions and valley polarized correlated insulators in twisted double bilayer graphene
• Quantum Geometry and Stability of Moiré Flatband Ferromagnetism
• Imaging topological torus lattice from an electron crystal in twisted mono-bilayer graphene
• Tunable bandwidths and gaps in twisted double bilayer graphene system on the verge of correlations
• Topological Flat Bands and Correlated States in Twisted Monolayer-Bilayer Graphene
• TSTG I: Single-Particle and Many-Body Hamiltonians and Hidden Non-local Symmetries of Trilayer Moiré Systems with and without Displacement Field
• Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect
• Pressure induced gap modulation and topological transitions in twisted bilayer and double bilayer graphene
• Magic-Angle Twisted Symmetric Trilayer Graphene as Topological Heavy Fermion Problem
• Exciton Proliferation and Fate of the Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: Applications to twisted double-bilayer graphene
• Tunable ferromagnetism at non-integer filling of a moiré superlattice
• Twistronics in graphene-based van der Waals structures
• Fragile topology in line-graph lattices with two, three, or four gapped flat bands
• Detection of graphene's divergent orbital diamagnetism at the Dirac point
• Hofstadter butterfly and the quantum Hall effect in twisted double bilayer graphenes
• Correlated Insulating Phases in the Twisted Bilayer Graphene
• Spin polarized nematic order, quantum valley Hall states, and field tunable topological transitions in twisted multilayer graphene systems
• Moiré disorder effect in twisted bilayer graphene
• Spectroscopic visualization of flat bands in magic-angle twisted monolayer-bilayer graphene: localization-delocalization coexisting electronic states
• Landau Levels as a Probe for Band Topology in Graphene Moiré Superlattices
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Current-induced reversal of anomalous Hall conductance in twisted bilayer graphene
• Magnetic Josephson Junctions and Superconducting Diodes in Magic Angle Twisted Bilayer Graphene
• Lattice Collective Modes from a Continuum Model of Magic-Angle Twisted Bilayer Graphene
• Valley-selective Floquet Chern Flat Bands in Twisted Multilayer Graphene
• Magnon magic angles and tunable Hall conductivity in 2D twisted ferromagnetic bilayers
• Pair density wave and loop current promoted by van Hove singularities in moiré systems
• Moiré lattice effects on the orbital magnetic response of twisted bilayer graphene and Condon instability
• Combined minivalley and layer control in twisted double bilayer graphene
• Metallic Network of Topological Domain Walls
• Emergence of Chern insulating states in non-Magic angle twisted bilayer graphene
• Electrically tuned topology and magnetism in twisted bilayer MoTe${}_2$ at ${\nu }_h=1$
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• Landau Levels of the Euler Class Topology
• Pair density wave and reentrant superconducting tendencies originating from valley polarization
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• High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems
• Chiral Decomposition of Twisted Graphene Multilayers with Arbitrary Stacking
• Quantum Valley Hall effect without Berry curvature
• Trions in Twisted Bilayer Graphene
• Electronic structure of 30° twisted double bilayer graphene
• Valley-Current Splitter in Minimally Twisted Bilayer Graphene
• Spin Liquids and Pseudogap Metals in $SU(4)$ Hubbard Model in Moiré Superlattice
• Perpendicular electric field drives Chern transitions and layer polarization changes in Hofstadter bands
• Phase diagram and orbital Chern insulator in twisted double bilayer graphene
• Observation of time-reversal symmetric Hall effect in graphene-WSe2 heterostructures at room temperature
• Topological Mixed Valence Model for Twisted Bilayer Graphene
• Unconventional sequence of correlated Chern insulators in magic-angle twisted bilayer graphene
• Dirac Magic and Lifshitz Transitions in AA-Stacked Twisted Multilayer Graphene
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• Optical imprinting of superlattices in two-dimensional materials
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• Generic "Unnecessary" Quantum Critical Points with Minimal Degrees of Freedom
• Observation of first-order quantum phase transitions and ferromagnetism in twisted double bilayer graphene
• Superconductivity in twisted multilayer graphene: a smoking gun in recent condensed matter physics
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• Intrinsic torque on the orbital angular momentum in an electric field
• Chern-insulator phases and spontaneous spin and valley order in a moiré lattice model for magic-angle twisted bilayer graphene
• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors
• Mesoscopic Electronic Transport in Twisted Bilayer Graphene
• Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene
• Vertical transverse transport induced by hidden in-plane Berry curvature in two dimensions
• Magic momenta and three dimensional Landau levels from a three dimensional graphite moiré superlattice
• Topological Mixed Valence Model in Magic-Angle Twisted Bilayer Graphene
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Quantum anomalous, spin, and valley Hall effects in pentalayer rhombohedral graphene moiré superlattices
• Absence of Edge States in The Valley Chern Insulator in Moiré Graphene
• Effects of Boundary on Orbital Magnetization for a Bilayer System with Different Chern Numbers
• Competing magnetic states on the surface of multilayer ABC-stacked graphene
• Tunable moire spinons in magnetically encapsulated twisted van der Waals quantum spin-liquids
• Tunneling chirality Hall effect in type-I Weyl semimetals
• Quantum valley Hall states in low-buckled counterparts of graphene bilayer
• Orbital Gravito-Magnetoelectric response and Orbital magnetic quadrupole moment correction
• Quantum oscillations in field-induced correlated insulators of a moiré superlattice
• Quantum Hall effects of exciton condensate in topological flat bands
• Moiré fractals in twisted graphene layers
• Emergence of intrinsically isolated flat bands and their topology in fully relaxed twisted multi-layer graphene
• Chern-Textured Exciton Insulators with Valley Spiral Order in Moiré Materials
• Moiré band theory for M-valley twisted transition metal dichalcogenides
• Orbital Magnetization under an Electric Field and Orbital Magnetoelectric Polarizabilty for a Bilayer Chern System
• Bilayer twisting as a mean to isolate connected flat bands in a Kagome lattice through Wigner crystallization
• Topologically nontrivial and trivial flat bands via weak and strong interlayer coupling in twisted bilayer honeycomb optical lattices for ultracold atoms
• Electron interactions in strain-induced zero-energy flat band in twisted bilayer graphene near the magic angle
• Emergent Symmetry and Valley Chern Insulator in Twisted Double-Bilayer Graphene
• Numerical Study of Disorder on the Orbital Magnetization in Two Dimensions
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
• Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch
• Topological phase transition from periodic edge states in moiré superlattices
• Tunable atomically enhanced moiré Berry curvatures in twisted triple bilayer graphene
• Shift current response in twisted double bilayer graphenes
• Perpendicular electronic transport and moiré-induced resonance in twisted interfaces of three-dimensional graphite
• Energy Spectrum Theory of Incommensurate Systems
• Particle-hole asymmetric phases in doped twisted bilayer graphene
• Electronic states at twist stacking faults in rhombohedral graphite
• Hofstadter Butterfly in Graphene
• Faraday rotations, ellipticity and circular dichroism in the magneto-optical spectrum of moiré superlattices
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides
• Invisible flat bands on a topological chiral edge