Stackings and effective models of bilayer dice lattices

Abstract

We introduce and classify nonequivalent commensurate stackings for bilayer dice or ${\mathcal{T}}_3$ lattice. For each of the four stackings with vertical alignment of sites in two layers, a tight-binding model and an effective model describing the properties in the vicinity of the threefold band-crossing points are derived. Focusing on these band-crossing points, we found that although the energy spectrum remains always gapless, depending on the stacking, different types of quasiparticle spectra arise. They include those with flat, tilted, anisotropic semi-Dirac, and $C_3$-corrugated energy bands. We use the derived tight-binding models to calculate the density of states and the spectral function. The corresponding results reveal drastic redistribution of the spectral weight due to the inter-layer coupling that is unique for each of the stackings.

arXiv comment15 pages, 9 multi-panel figures

References in corpus (32)

• Electric Field Effect in Atomically Thin Carbon Films
• Topological Insulators
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Weyl and Dirac Semimetals in Three Dimensional Solids
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Moire bands in twisted double-layer graphene
• Tuning superconductivity in twisted bilayer graphene
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Observation of the chiral anomaly induced negative magneto-resistance in 3D Weyl semi-metal TaAs
• Graphene bilayer with a twist: electronic structure
• The electronic properties of bilayer graphene
• Flat Bands in Slightly Twisted Bilayer Graphene
• Graphene Bilayers with a Twist
• Artificial flat band systems: from lattice models to experiments
• Aharonov-Bohm cages in two-dimensional structures
• Dirac vs. Weyl in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena
• Nematicity and Competing Orders in Superconducting Magic-Angle Graphene
• Optical and magneto-optical far-infrared properties of bilayer graphene
• Zero modes of tight binding electrons on the honeycomb lattice
• From dia- to paramagnetic orbital susceptibility of Dirac cones
• Quantum Monte Carlo Calculation of the Binding Energy of Bilayer Graphene
• Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
• Phase Diagram of the Bose-Hubbard Model with T_3 symmetry
• Particle-Hole Symmetries in Condensed Matter
• Electronic states of pseudospin-1 fermions in dice lattice ribbons
• Tunable orbital susceptibility in $\alpha$-${\mathcal{T}}_3$ tight-binding models
• Vortex correlations in a fully frustrated two-dimensional superconducting network
• Gap generation and flat band catalysis in dice model with local interaction
• Many-Body Effects and Optical Properties of Single- and Double Layer $\alpha$-${\mathcal{T}}_3$ Lattices
• Optical conductivity of bilayer dice lattices

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• Moiré semiconductors on twisted bilayer dice lattice
• Generation of isolated flat bands with tunable numbers through Moiré engineering
• Emergent topology of flat bands in a twisted bilayer $\alpha$-$T_3$ lattice
• Topological Properties of Bilayer $\alpha -T_3$ Lattice Induced by Polarized Light
• Geometry-Driven Moiré Engineering in Twisted Bilayers of High-Pseudospin Fermions