Topologically Protected Zero Modes in Twisted Bilayer Graphene

Abstract

We show that the twisted graphene bilayer can reveal unusual topological properties at low energies, as a consequence of a Dirac-point splitting. These features rely on a symmetry analysis of the electron hopping between the two layers of graphene and we derive a simplified effective low-energy Hamiltonian which captures the essential topological properties of twisted bilayer graphene. The corresponding Landau levels peculiarly reveal a degenerate zero-energy mode which cannot be lifted by strong magnetic fields.

5 pages, 3 figures; published version

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Cited by in corpus (86)

• Graphene Bilayers with a Twist
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• Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene
• A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
• Ab-Initio Theory of Moiré Superlattice Bands in Layered Two-Dimensional Materials
• Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
• Non-Abelian gauge potentials in graphene bilayers
• Strain-induced Evolution of Electronic Band Structures in a Twisted Graphene Bilayer
• Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization not Mott Insulation
• Helical networks in twisted bilayer graphene under interlayer bias
• Quantum Hall Effect, Screening and Layer-Polarized Insulating States in Twisted Bilayer Graphene
• Band Symmetries and Singularities in Twisted Multilayer Graphene
• Helical Network Model for Twisted Bilayer Graphene
• Flat bands and perfect metal in trilayer moiré graphene
• Structure of twisted and buckled bilayer graphene
• Observation of Helical Edge States and Fractional Quantum Hall Effect in a Graphene Electron-hole Bilayer
• Optical Conductivity of Twisted Bilayer Graphene
• Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene
• Superlattice structures in twisted bilayers of folded graphene
• Chiral Tunnelling in Twisted Graphene Bilayer
• Topological Floquet Engineering of Twisted Bilayer Graphene
• Interlayer coupling in rotationally faulted multilayer graphenes
• Dodecagonal bilayer graphene quasicrystal and its approximants
• Electronic topological transition in sliding bilayer graphene
• Landau Level Degeneracy in Twisted Bilayer Graphene: Role of Symmetry Breaking
• Pseudospin Vortex Ring with a Nodal Line in Three Dimensions
• Manipulation of Dirac points in graphene-like crystals
• Winding vector: how to annihilate two Dirac points with the same charge
• Topological phases in gated bilayer graphene: Effects of Rashba spin-orbit coupling and exchange field
• Externally controlled band gap in twisted bilayer graphene
• Floquet-Engineered Topological Flat Bands in Irradiated Twisted Bilayer Graphene
• Finite size effects on topological interface states in one-dimensional scattering systems
• Quantum Oscillations in Nodal Line Systems
• Magneto-optics of a Weyl semimetal beyond the conical band approximation: the case study of TaP
• Creating Magnetic Fields in excess of 1000 T by Misoriented Stacking in a Graphene Bilayer
• Angle Dependence of Landau Level Spectrum in Twisted Bilayer Graphene
• Polarization resolved magneto-Raman scattering of graphene-like domains on natural graphite
• Transport across twist angle domains in moiré graphene
• Twisted bilayer graphene in a parallel magnetic field
• Bilayer graphene with parallel magnetic field and twisting: Phases and phase transitions in a highly tunable Dirac system
• Magnetic spectrum of trigonally warped bilayer graphene - semiclassical analysis, zero modes, and topological winding numbers
• Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder
• Carrier transport theory for twisted bilayer graphene in the metallic regime
• Enhanced Intervalley Scattering of Twisted Bilayer Graphene by Periodic AB Stacked Atoms
• Mass and chirality inversion of a Dirac cone pair in Stückelberg interferometry
• Friedel oscillations at the Dirac-cone-merging point in anisotropic graphene
• Merging Dirac points and topological phase transitions in the tight-binding model on the generalized honeycomb lattice
• Artificial graphenes: Dirac matter beyond condensed matter
• Berry Phase Transition in Twisted Bilayer Graphene
• Graphene: Kinks, Superlattices, Landau levels, and Magnetotransport
• Coexistence and competition of nematic and gapped states in bilayer graphene
• Magic angle twisted bilayer graphene as a highly efficient quantum Otto engine
• Magnetic Breakdown in Twisted Bilayer Graphene
• Piezoelectricity in asymmetrically strained bilayer graphene
• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• Band spectrum is D-brane
• Transparent mirror effect in twist-angle-disordered bilayer graphene
• Tunable zero-energy transmission resonances in shifted graphene bilayer
• Twisted bilayer graphene: low-energy physics, electronic and optical properties
• Inherited topological superconductivity in two-dimensional Dirac semimetals
• Geometric phase in Stückelberg interferometry
• Antiferromagnetism and chiral d-wave superconductivity from an effective $t-J-D$ model for twisted bilayer graphene
• Electronic properties of strained double-Weyl systems
• Magic momenta and three dimensional Landau levels from a three dimensional graphite moiré superlattice
• Small scale rotational disorder observed in epitaxial graphene on SiC(0001)
• Nodal Surfaces in Photoemission from Twisted Bilayer Graphene
• Two-Dimensional Thouless Pumping of Ultracold Fermions in Obliquely Introduced Optical Superlattice
• Confined states in graphene quantum blisters
• Wigner crystallization at large fine structure constant
• Band structure and band topology in twisted homotrilayer transition metal dichalcogenides
• Realization and transport investigation of a single layer-twisted bilayer graphene junction
• Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials
• Probing Layer Localization in Twisted Graphene Bilayers via Cyclotron Resonance
• Capturing magic angles in twisted bilayer graphene from information theory markers
• Magnetoconductance of the Corbino disk in graphene: Chiral tunneling and quantum interference in the bilayer case
• Experimental evidence of the topological obstruction in twisted bilayer graphene
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• Topological phase diagram of twisted bilayer graphene as a function of the twist angle
• Van der Waals Heterostructure Pt${}_2$HgSe${}_3$/CrI${}_3$ for Topological Valleytronics
• Mechanism of skyrmion condensation and pairing for twisted bi-layer graphene
• Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields
• Competing topological phases in few-layer graphene