Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime

Abstract

The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moiré bands for twisted bilayer graphene (TBG) at small twist angles. We derive a generalized continuum model for TBG near any commensurate twist angle, which is characterized by complex interlayer hoppings at commensurate $AA$ stackings (rather than the real hoppings in the BM model), a real interlayer hopping at commensurate $AB/BA$ stackings, and a global energy shift. The complex phases of the $AA$ stacking hoppings and the twist angle together define a single angle parameter ${\varphi }_0$. We compute the model parameters for the first six distinct commensurate TBG configurations, among which the $38.2^{\circ }$ configuration may be within experimentally observable energy scales. We identify the first magic angle for any ${\varphi }_0$ at a condition similar to that of the BM model. At this angle, the lowest two moiré bands at charge neutrality become flat except near the ${\mathbf{\Gamma }}_M$ point and retain fragile topology but lose particle-hole symmetry. We further identify a hypermagic parameter regime centered at ${\varphi }_0=\pm \pi /2$ where many moiré bands around charge neutrality (often $8$ or more) become flat simultaneously. Many of these flat bands resemble those in the kagome lattice and $p_x$, $p_y$ 2-orbital honeycomb lattice tight-binding models.

49 pages, 22 figures, accepted by Physical Review B

References in corpus (19)

• The electronic properties of graphene
• High temperature fractional quantum Hall states
• Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Electric field tunable unconventional superconductivity in alternating twist magic-angle trilayer graphene
• Superconductivity in rhombohedral trilayer graphene
• Evidence for unconventional superconductivity in twisted bilayer graphene
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Hofstadter subband ferromagnetism and symmetry broken Chern insulators in twisted bilayer graphene
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
• One-Dimensional Luttinger Liquids in a Two-Dimensional Moiré Lattice
• Twisted bilayer graphene.VI. An Exact Diagonalization Study of Twisted Bilayer Graphene at Non-Zero Integer Fillings
• Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a $k\cdot p$ 2-Band model
• Flat bands and perfect metal in trilayer moiré graphene
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles

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• Terahertz Circular Dichroism in Commensurate Twisted Bilayer Graphene
• Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands
• Intrinsically-multilayer moiré heterostructures
• Quantum Valley and Sub-valley Hall Effect in the Large Angle Twisted Bilayer Graphene
• Kagome and honeycomb flat bands in moiré graphene
• Intrinsic and extrinsic photogalvanic effects in twisted bilayer graphene
• Emergence of flat bands in the quasicrystal limit of boron nitride twisted bilayers
• Emergent Hyper-Magic Manifold in Twisted Kitaev Bilayers
• Designing Topological High-Order Van Hove Singularities: Twisted Bilayer Kagomé
• Sliding Luttinger Liquid and Topological Flat Bands in Symmetry Mismatched Moiré Interfaces
• Topological domain-wall states from Umklapp scattering in twisted bilayer graphene
• Incommensurate Twisted Bilayer Graphene: emerging quasi-periodicity and stability