Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level

Abstract

We study the chirally symmetric continuum model (CS-CM) of the twisted bilayer graphene. The equation on a flat band could be interpreted as a Dirac equation on a torus in the external non-abelian magnetic field. We prove that the existence of the flat band implies that the wave-function has a zero and vice verse. We found a hidden solution in the CS-CM model that has a pole instead of a zero. Our main result is that in the basis of the flat band and hidden wave functions the flat band could be interpreted as Landau level in the external magnetic field. From that interpretation we show the existence of extra flat bands in the magnetic field.

arXiv commentv1: 4+4 pages, no figures; v2: minor improvements

References in corpus (41)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Origin of Magic Angles in Twisted Bilayer Graphene
• Topological insulators in twisted transition metal dichalcogenide homobilayers
• Continuum Model of the Twisted Bilayer
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• Theory of phonon-mediated superconductivity in twisted bilayer graphene
• Topological Superconductivity in Twisted Multilayer Graphene
• Nearly Flat Chern Bands in Moiré Superlattices
• Band Structure of Twisted Bilayer Graphene: Emergent Symmetries, Commensurate Approximants and Wannier Obstructions
• Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
• Electrostatic effects, band distortions and superconductivity in twisted graphene bilayers
• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene
• Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene
• The pseudo-Landau-level representation of twisted bilayer graphene: band topology and the implications on the correlated insulating phase
• Non-Abelian gauge potentials in graphene bilayers
• Strong Correlations and d+id Superconductivity in Twisted Bilayer Graphene
• Moire Butterflies
• Pressure dependence of the magic twist angle in graphene superlattices
• Mean-field theory for superconductivity in twisted bilayer graphene
• Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions
• Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene
• Charge-transfer insulation in twisted bilayer graphene
• Helical Network Model for Twisted Bilayer Graphene
• Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene
• Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene
• Heterostrain engineering on twisted graphene bilayer around the first magic angle
• Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene
• Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach
• The nature of correlations in the insulating states of twisted bilayer graphene
• Transport measurements in twisted bilayer graphene: Electron-phonon coupling and Landau level crossing
• Energy minimization of 2D incommensurate heterostructures
• Emergent Superconductivity in the weak Mott insulator phase of bilayer Graphene Moiré Superlattice
• Multiband Mechanism for the Sign Reversal of Coulomb Drag Observed in Double Bilayer Graphene Heterostructures
• Raman Scattering as a Selective Probe of Chiral Electronic Excitations in Bilayer Graphene
• On magic angles and band flattening in twisted bilayer graphene
• Current-Induced Heat Transfer in Double-Layer Graphene
• Enhanced Robustness of Zero-line Modes in Graphene via a Magnetic Field

Cited by in corpus (21)

• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction
• Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a $2\times 2$ matrix operator and physical origin of flat-bands at magic angles
• 3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect
• Origin of band flatness and constraints of higher Chern numbers
• Symmetries as the guiding principle for flattening bands of Dirac fermions
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization
• Beyond the Berry Phase: Extrinsic Geometry of Quantum States
• Narrow bands in magnetic field and strong-coupling Hofstadter spectra
• Re-entrant magic-angle phenomena in twisted bilayer graphene in integer magnetic fluxes
• Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
• Helical trilayer graphene in magnetic field: Chern mosaic and higher Chern number ideal flat bands
• Supersymmetry dictated topology in periodic gauge fields and realization in strained and twisted 2D materials
• Designing Flat Bands and Pseudo-Landau Levels in GaAs with Patterned Gates