Chiral Flat Bands: Existence, Engineering and Stability

Abstract

We study flat bands in bipartite tight-binding networks with discrete translational invariance. Chiral flat bands with chiral symmetry eigenenergy E = 0 and host compact localized eigenstates for finite range hopping. For a bipartite network with a majority sublattice chiral flat bands emerge. We present a simple generating principle of chiral flat band networks and as a showcase add to the previously observed cases a number of new potentially realizable chiral flat bands in various lattice dimensions. Chiral symmetry respecting network perturbations - including disorder and synthetic magnetic fields - preserve both the flatband and the modified compact localized states. Chiral flatbands are spectrally protected by gaps, and pseudogaps in the presence of disorder due to Griffiths effects.

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Cited by in corpus (85)

• Artificial flat band systems: from lattice models to experiments
• Classification of flat bands according to the band-crossing singularity of Bloch wave functions
• Unconventional Flatband Line States in Photonic Lieb Lattices
• Many-Body Flatband Localization
• Disordered flat bands on the kagome lattice
• Flat bands in fractal-like geometry
• Bimorphic Floquet Topological Insulators
• Compact localized states and flat bands from local symmetry partitioning
• Universal $d=1$ flatband generator from compact localized states
• Nontrivial topological flat bands in a diamond-octagon lattice geometry
• Flatband generator in two dimensions
• Flat bands by latent symmetry
• Flat bands and nontrivial topological properties in an extended Lieb lattice
• Topological flat Wannier-Stark bands
• Observation of Photonic Chiral Flatbands
• General construction of flat bands with and without band crossings based on wave function singularity
• Flatband Line States in Photonic Super-Honeycomb Lattices
• Flat band in two-dimensional non-Hermitian optical lattices
• Disorder perturbed Flat Bands I: Level density and Inverse Participation Ratio
• Designing flat-band tight-binding models with tunable multifold band touching points
• Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks
• Interplay of disorder and interactions in a flat-band supporting diamond chain
• Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices
• Compact Discrete Breathers on Flat Band Networks
• Flat-band-based multifractality in the all-band-flat diamond chain
• High-order Van Hove singularities and their connection to flat bands
• Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity
• Flat bands with band crossings enforced by symmetry representation
• Disorder effects in the two-dimensional Lieb lattice and its extensions
• Non-Compact Atomic Insulators
• Localization, phases and transitions in the three-dimensional extended Lieb lattices
• Non-Hermitian flatband generator in one dimension
• Metal-insulator transition in infinitesimally weakly disordered flatbands
• Wannier-Stark flatbands in Bravais lattices
• Many-body localization transition from flatband fine-tuning
• Microwave photonic crystals as an experimental realization of a combined honeycomb-kagome lattice
• Engineering topological phase transition and Aharonov-Bohm caging in a flux-staggered lattice
• Flat bands and entanglement in the Kitaev ladder
• Necessary and sufficient conditions for flat bands in $M$-dimensional $N$-band lattices with complex-valued nearest-neighbour hopping
• Flat Band Induced Metal-Insulator Transitions for Weak Magnetic Flux and Spin-Orbit Disorder
• Highly degenerate photonic flat bands arising from complete graph configurations
• Dynamical quantum phase transitions on cross-stitch flat band networks
• Anti-$\mathcal{P}\mathcal{T}$ flatbands
• Impact of strong correlations on a band topological insulator on the Lieb lattice
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• Unconventional delocalization in a family of 3D Lieb lattices
• Going beyond the Chandrasekhar-Clogston limit in a flat-band superconductor
• Dipole-dipole interactions mediated by a photonic flat band
• Periodic and aperiodic dynamics of flat bands in diamond-octagon lattice
• Electronic structure of a graphene-like artificial crystal of $NdNi{O}_3$
• Compact localised states in magnonic Lieb lattices
• Resonant frequencies and spatial correlations in frustrated arrays of Josephson type nonlinear oscillators
• Flat Bands and Compact Localised States: A Carrollian roadmap
• Tunable Aharonov-Bohm cages through anti-$\mathcal{P}\mathcal{T}$-symmetric imaginary couplings
• Flat-band quantum communication induced by disorder
• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
• Designing single and degenerate flat bands in the kagome lattice with long-range hopping
• Flux modulated flat band engineering in square-kagome ladder network
• Singular flat bands in the modified Haldane-Dice model
• Van Hove bound states in the continuum: Localised subradiant states in finite open lattices
• A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system
• Engineering flux-controlled flat bands and topological states in a Stagome lattice
• Emergent chiral symmetry in non-bipartite kagome and pyrochlore lattices with spin-orbit coupling
• Quantum percolation on Lieb Lattices
• Complete escape from localization on a hierarchical lattice: A Koch fractal with all states extended
• Trapping Hard-Core Bosons in Flatband Lattices
• Analytical study of quasi-one dimensional flat band networks and slow light analogue
• Mirror Chern numbers in the hybrid Wannier representation
• RKKY plateau in zero- and one-dimensional triangular Kagome lattice models
• Flat Bands in Three-dimensional Lattice Models with Non-trivial Hopf Index
• Fragmentation, Zero Modes, and Collective Bound States in Constrained Models
• Spin-selective Aharonov-Casher caging in a topological quantum network
• Quantum engineering for compactly localized states in disordered Lieb lattices
• How to realize compact and non-compact localized states in disorder-free hypercube networks
• Electronic interactions in a vacancy-engineered honeycomb lattice: Transition from a nodal-line semimetal to a magnetic insulator
• Chirally-protected state manipulation by tuning one-dimensional statistics
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
• Symmetry-protected flatband condition for Hamiltonians with local symmetry
• Robust Orbital-Selective Flat Bands in Transition-Metal Oxychlorides
• Resonant cavity-QED with chiral flat bands
• Flat bands and band touching from real-space topology in hyperbolic lattices
• Weak-coupling bound states in semi-infinite topological waveguide QED
• Compact localized currents in flat bands with broken time-reversal symmetry
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• Flat band mediated photon-photon interactions in 2D waveguide QED networks