Chiral model of twisted bilayer graphene realized in a monolayer

Abstract

We demonstrate that a single layer of graphene subject to a superlattice potential nearly commensurate to a $\sqrt{3}\times \sqrt{3}$ supercell exactly maps to the chiral model of twisted bilayer graphene, albeit with half as many degrees of freedom. We comprehensively review the properties of this ``half-chiral model,'' including the interacting phases stabilized at integer fillings and the effects of substrate-induced symmetry breaking. We list candidate substrates that could produce a superlattice potential on graphene with the correct periodicity to access the flat band limit. Experimental measurements on a half-chiral moire heterostructure, in which valley-skyrmions cannot form, could yield insights on the physics they mediate in twisted bilayer graphene.

References in corpus (50)

• 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
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Graphene bilayer with a twist: electronic structure
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• Graphene Bilayers with a Twist
• Origin of Magic Angles in Twisted Bilayer Graphene
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene
• Chern Insulators and Topological Flat-bands in Magic-angle Twisted Bilayer Graphene
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
• Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
• The pseudo-Landau-level representation of twisted bilayer graphene: band topology and the implications on the correlated insulating phase
• Band Structure Engineering of 2D Materials using Patterned Dielectric Superlattices
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Hofstadter subband ferromagnetism and symmetry broken Chern insulators in twisted bilayer graphene
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene
• 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
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• 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
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Anisotropic band flattening in graphene with 1D superlattices
• Topological and stacked flat bands in bilayer graphene with a superlattice potential
• Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators
• Topological superconductivity with deformable magnetic skyrmions
• A moiré superlattice on the surface of a topological insulator
• Skyrmion Superconductivity: DMRG evidence for a topological route to superconductivity
• Engineering high quality graphene superlattices via ion milled ultra-thin etching masks
• Topological superconductivity in doped magnetic moiré semiconductors
• Supermoiré low-energy effective theory of twisted trilayer graphene
• Mathematics of magic angles in a model of twisted bilayer graphene
• Gate-tunable flat bands in van der Waals patterned dielectric superlattices
• Unconventional superconductivity due to interband polarization
• Multilayer graphene with a superlattice potential
• Symmetries as the guiding principle for flattening bands of Dirac fermions
• Matrix Product State description of the Halperin States
• Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
• Designer Meron Lattice on the Surface of a Topological Insulator
• Tailoring Dirac fermions by in-situ tunable high-order moire pattern in graphene-monolayer xenon heterostructure
• Magic angle conditions for twisted 3D topological insulators
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• Dirac Fermion Cloning, Moir$\acute{\mathbf{e}}$ Flat Bands and Magic Lattice Constants in Epitaxial Monolayer Graphene
• Optoelectronic Fingerprints of Interference between Different Charge Carriers in Graphene Superlattices and Analogies to Twisted Graphene Bilayers
• Intrinsically-multilayer moiré heterostructures

Cited by in corpus (13)

• Ideal Chern bands are Landau levels in curved space
• Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
• Sublattice structure and topology in spontaneously crystallized electronic states
• Bridging the small and large in twisted transition metal dicalcogenide homobilayers: a tight binding model capturing orbital interference and topology across a wide range of twist angles
• Gate-tunable topological phases in superlattice modulated bilayer graphene
• Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted WSe${}_2$
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Topologically protected flatness in chiral moiré heterostructures
• Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Quantum simulation of honeycomb lattice model by high-order moiré pattern
• Efficient prediction of topological superlattice bands with spin-orbit coupling