Exotic electronic states in the world of flat bands: from theory to material

Abstract

It has long been noticed that special lattices contain single-electron flat bands (FB) without any dispersion. Since the kinetic energy of electrons is quenched in the FB, this highly degenerate energy level becomes an ideal platform to achieve strongly correlated electronic states, such as magnetism, superconductivity and Wigner crystal. Recently, the FB has attracted increasing interests, because of the possibility to go beyond the conventional symmetry-breaking phases, towards topologically ordered phases, such as lattice versions of fractional quantum Hall states. This article reviews different aspects of FBs in a nutshell. Starting from the standard band theory, we aim to bridge the frontier of FBs with the textbook solid-state physics. Then, based on concrete examples, we show the common origin of FBs in terms of destructive interference, and discuss various many-body phases associated with such a singular band structure. In the end, we demonstrate real FBs in quantum frustrated materials and organometallic frameworks.

17 pages, 10 figures

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Cited by in corpus (73)

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• Excitonic Condensate in Flat Valence and Conduction Bands of Opposite Chirality
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• Giant Anomalous Hall Effect due to Double-Degenerate Quasi Flat Bands
• Designing flat-band tight-binding models with tunable multifold band touching points
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• Correlated Electronic Structure and Incipient Flat Bands of the Kagome Superconductor CsCr3Sb5
• Robust flat bands in RCo5 (R=rare earth) compounds
• Topological origin of flat-bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions
• Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
• Topological States in Dimerized Quantum-Dot Chains Created by Atom Manipulation
• Observation of Flat Bands and Dirac Cones in a Pyrochlore Lattice Superconductor
• Compactly Supported Wannier Functions and Strictly Local Projectors
• Topological inverse Anderson insulator
• Isolated Flat Bands and Physics of Mixed Dimensions in a 2D Covalent Organic Framework
• Evolution of ultra-flat band in van der Waals kagome semiconductor Pd3P2(S1-xSex)8
• Prediction of polarization vortices, charge modulation, flat bands, and moiré magnetism in twisted oxide bilayers
• Line-graph-lattice crystal structures of stoichiometric materials
• Electronic band structures of topological kagome materials
• Dispersion-driven ferromagnetism in a flat-band Hubbard system
• Symmetry-protected Topological Phases in Spinful Bosons with a Flat Band
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Catalogue of Flat-Band Stoichiometric Materials
• Hubbard models and state preparation in an optical Lieb lattice
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• Extensibility of Hohenberg-Kohn Theorem to general quantum systems
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• Hund's coupling-assisted ferromagnetic percolation transition in a multiorbital flat band
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• Excitation spectra of strongly interacting bosons in the flat-band Lieb lattice
• High Chern numbers and topological flat bands in high-field polarized Kitaev magnets on the star lattice
• Three-body problem in a multiband Hubbard model
• Moiré semiconductors on twisted bilayer dice lattice
• Nonlinear Bloch-Zener oscillations for Bose-Einstein condensates in a Lieb optical lattice
• Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
• Dynamical Signatures of Liouvillian Flat Band
• Doping induced multiferroicity and quantum anomalous Hall effect in $\alpha$-In${}_2$Se${}_3$ thin films
• Effect of electron- and hole-doping on properties of kagome-lattice ferromagnet Fe3Sn2
• Isolated nearly flat higher Chern band in monolayer transition metal trihalides
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Stability of $(N+1)$-body fermion clusters in multiband Hubbard model
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Hybrid Interference Induced Flat Band Localization in Bipartite Optomechanical Lattices
• van Hove Singularity-Driven Emergence of Multiple Flat Bands in Kagome Superconductors
• Correlated physics in an artificial triangular anti-dot lattice
• Correlated metallic two-particle bound states in Wannier--Stark flatbands
• Anomalous Bilayer Quantum Hall Effect
• Anomalous Hall effect in the coplanar antiferromagnetic coloring-triangular lattice
• Singular angular magnetoresistance and sharp resonant features in a high-mobility metal with open orbits, ReO3
• Flat Band Generation through Interlayer Geometric Frustration in Intercalated Transition Metal Dichalcogenides
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
• Trends in Bandgap of Epitaxial $\text{A}$${}_2$$\text{B}$${}_2$O${}_7$ ($\text{A}$ = Sn, Pb; $\text{B}$ = Nb, Ta) Films Fabricated by Pulsed Laser Deposition
• One-dimensional Dexter-type excitonic topological phase transition
• Non-Abelian line graph: A generalized approach to flat bands
• Quantum dots on the InAs(110) cleavage surface created by atom manipulation
• Robust Orbital-Selective Flat Bands in Transition-Metal Oxychlorides
• Dynamical Orbital Angular Momentum Induced by Circularly Polarized Phonons
• Topological Degeneracy Induced Flat Bands in two-Dimensional Holed Systems
• Symmetry-Based Real-Space Framework for Realizing Flat Bands and Unveiling Nodal-Line Touchings
• Realization of Nearly Dispersionless Bands with Strong Orbital Anisotropy from Destructive Interference in Twisted Bilayer MoS2
• Fractional spin Josephson effect in topological spin superconductors
• Sublattice polarization and filamentary superconductivity in strained graphene