A simple method to construct Flat Band lattices

Abstract

We develop a simple and general method to construct arbitrary Flat Band lattices. We identify the basic ingredients behind zero-dispersion bands and develop a method to construct extended lattices based on a consecutive repetition of a given mini-array. The number of degenerated localized states is defined by the number of connected mini-arrays times the number of modes preserving the symmetry at a given connector site. In this way, we create one or more (depending on the lattice geometry) complete degenerated Flat Bands for quasi-one and two-dimensional systems. We probe our method by studying several examples, and discuss the effect of additional interactions like anisotropy or nonlinearity. At the end, we test our method by studying numerically a ribbon lattice using a continuous description.

11 pages, 11 figures

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• Flatband generator in two dimensions
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• Designer Flat Bands in Quasi-One-Dimensional Atomic Lattices
• Nonlinear caging in All-Bands-Flat Lattices
• Quantum Caging in Interacting Many-Body All-Bands-Flat Lattices
• Designing flat-band tight-binding models with tunable multifold band touching points
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• Quantum network transfer and storage with compact localized states induced by local symmetries
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• Quantum localized states in photonic flat-band lattices
• Observation of Ground and Excited Flat Band States in Graphene Photonic Ribbons
• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• Perfect localization on flat band binary one-dimensional photonic lattices
• Quench dynamics of quantum spin models with flat bands of excitations
• Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field: Unconventional phase transitions in a two-dimensional isotropic Heisenberg model
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• Flat bands and compactons in mechanical lattices
• Single and double linear and nonlinear flatband chains: spectra and modes
• Anti-$\mathcal{P}\mathcal{T}$ flatbands
• Methods for constructing parameter-dependent flat band lattices
• Designer quantum states on a fractal substrate: compact localization, flat bands and the edge modes
• Symmetry-protected Topological Phases in Spinful Bosons with a Flat Band
• Resonant frequencies and spatial correlations in frustrated arrays of Josephson type nonlinear oscillators
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Tunable Aharonov-Bohm cages through anti-$\mathcal{P}\mathcal{T}$-symmetric imaginary couplings
• Flat bands and temperature-driven phase transition in quasi-one-dimensional zigzag chains
• Quantum collision theory in flat bands
• Flux modulated flat band engineering in square-kagome ladder network
• Compact Wannier Functions in One Dimension
• Flat-band engineering of quasi-one-dimensional systems via supersymmetric transformations
• Complete Delocalization in a Defective Periodic Structure
• Analytical study of quasi-one dimensional flat band networks and slow light analogue
• RKKY plateau in zero- and one-dimensional triangular Kagome lattice models
• Two-dimensional flat-band solitons in superhoneycomb lattices
• Mode conversion and resonant absorption in inhomogeneous materials with flat bands
• Fragmentation, Zero Modes, and Collective Bound States in Constrained Models
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
• Selective band interaction and long-range hopping in a structured environment with giant atoms
• Resonant cavity-QED with chiral flat bands
• Non-Hermitian Aharonov-Bohm Cage
• Nonlinear compact localized modes in flux-dressed octagonal-diamond photonic lattice
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Weak localization and universal conductance fluctuations in large area twisted bilayer graphene
• Symmetry-Based Real-Space Framework for Realizing Flat Bands and Unveiling Nodal-Line Touchings
• Decorated cluster lattices: a natural framework for classical spin liquids and flat bands
• Controlled transport based on multiorbital Aharonov-Bohm photonic caging
• Dissipation-Driven Transition of Particles from Dispersive to Flat Bands
• Compact localized currents in flat bands with broken time-reversal symmetry