Emergent topology of flat bands in a twisted bilayer $\alpha$-$T_3$ lattice

Abstract

We investigate an interesting interplay of destructive interference due to lattice geometry and band folding due to enlargement of the Brillouin zone in generating and subsequently modifying the band topology in a twisted bilayer $\alpha$-$T_3$ system. The pronounced degeneracy of the emergent flat band in the dice limit of the $\alpha$-$T_3$ lattice is removed on alignment with h-BN layers, resulting in the formation of sub-bands with varying topological characteristics. Remarkably, while the sub-band near charge neutrality exhibits a trivial behavior, a topologically non-degenerate singular sub-band emerges away from charge neutrality. The topological band remains isolated from the rest of the bands for a substantial area of the $\alpha -\theta$ plane (where $\alpha$ and $\theta$ correspond to the hopping ratio and twist angle respectively) while exhibiting multiple phase transitions as a function of the aforementioned parameters via hybridization with its nearest bands. We study the evolution of the hybrid Wannier charge center and the Chern number to characterize the different emergent topological phases. Finally, the degree of flatness of the topological band is studied as a function of both $\alpha$ and $\theta$ to explicitly show the influence of quantum interference and band folding on the width of the topological band.

arXiv comment17 pages, 14 figures

References in corpus (48)

• 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
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Origin of Magic Angles in Twisted Bilayer Graphene
• Dirac fermions and flat bands in the ideal kagome metal FeSn
• Electric Field Tunable Correlated States and Magnetic Phase Transitions in Twisted Bilayer-Bilayer Graphene
• Observation of a localized flat-band state in a photonic Lieb lattice
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Strange metal in magic-angle graphene with near Planckian dissipation
• Aharonov-Bohm cages in two-dimensional structures
• Wannier representation of Z_2 topological insulators
• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• Nearly Flat Chern Bands in Moiré Superlattices
• Nearly flat band with Chern number C=2 on the dice lattice
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• From dia- to paramagnetic orbital susceptibility of Dirac cones
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model
• Wannier Center Sheets in Topological Insulators
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Theories for the correlated insulating states and quantum anomalous Hall phenomena in twisted bilayer graphene
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Lattice models with exactly solvable topological hinge and corner states
• Interlayer interaction in general incommensurate atomic layers
• Magneto-optics of massless Kane fermions: Role of the flat band and unusual Berry phase
• Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a $k\cdot p$ 2-Band model
• Hall quantization and optical conductivity evolution with variable Berry phase in $\alpha$-$T_3$ model
• Correlated phases of bosons in the flat lowest band of the dice lattice
• Phase Diagram of the Bose-Hubbard Model with T_3 symmetry
• Photoinduced valley and electron-hole symmetry breaking in $\alpha$-$T_3$ lattice: The role of a variable Berry phase
• Floquet topological phase transition in $\alpha$-${\mathcal{T}}_3$ lattice
• Band structure of twisted bilayer graphene on hexagonal boron nitride
• Probing Topological signatures in an optically driven $\alpha$-$T_3$ Lattice
• From electrons to baby skyrmions in Chern ferromagnets: A topological mechanism for spin-polaron formation in twisted bilayer graphene
• Topological features of Haldane model on a dice lattice: role of flat band on transport properties
• Floquet engineering of topological phase transitions in quantum spin Hall $\alpha$-$T_3$ system
• Stackings and effective models of bilayer dice lattices
• Optical conductivity of bilayer dice lattices
• Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• Designing single and degenerate flat bands in the kagome lattice with long-range hopping
• Moiré semiconductors on twisted bilayer dice lattice
• Generation of isolated flat bands with tunable numbers through Moiré engineering
• An experimental scheme for determining the Berry phase in two-dimensional quantum materials with a flat band

Cited by in corpus (1)

• Moiré-driven equilibrium of perturbations in moiré systems