Geometric characterization of anomalous Landau levels of isolated flat bands
arXiv:2012.15132 · doi:10.1038/s41467-021-26765-z
Abstract
According to the Onsager's semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this expectation, including topological bands and flat bands with singular band crossings, whose wave functions possess some singularities. Here, we introduce a distinct class of flat band systems where anomalous Landau level spreading (LLS) appears outside the zero-field energy bounds, although the relevant wave function is nonsingular. The anomalous LLS of isolated flat bands are governed by the cross-gap Berry connection that measures the wave-function geometry of multi bands. We also find that symmetry puts strong constraints on the LLS of flat bands. Our work demonstrates that an isolated flat band is an ideal system for studying the fundamental role of wave-function geometry in describing magnetic responses of solids.
arXiv comment10+8 pages, 5+3 figures
References in corpus (42)
- Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
- Topological Photonics
- Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
- Quantum Copying: Beyond the No-Cloning Theorem
- Quantized circular photogalvanic effect in Weyl semimetals
- Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
- Observation of bound states in Lieb photonic lattices
- Synthetic gauge fields in synthetic dimensions
- Flat bands and Wigner crystallization in the honeycomb optical lattice
- All "Magic Angles" Are "Stable" Topological
- Experimental realization and characterization of an electronic Lieb lattice
- Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
- Topological quantum matter in synthetic dimensions
- Fragile Topology and Wannier Obstructions
- Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
- Bosonic Condensation and Disorder-Induced Localization in a Flat Band
- Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice
- Topological states in engineered atomic lattices
- Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
- Classification of flat bands according to the band-crossing singularity of Bloch wave functions
- Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling
- Experimental band structure spectroscopy along a synthetic dimension
- Flat bands, Dirac cones and atom dynamics in an optical lattice
- Hofstadter butterflies for flat bands
- Abelian and Non-Abelian Quantum Geometric Tensor
- Realization of Lieb Lattice in Covalent-organic Frameworks with Tunable Topology and Magnetism
- Observation of nodal-line semimetal with ultracold fermions in an optical lattice
- The Landau Level of Fragile Topology
- Compactly-supported Wannier functions and algebraic -theory
- Hofstadter Topology: Non-crystalline Topological Materials at High Flux
- Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
- The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models
- Realization of robust boundary modes and non-contractible loop states in photonic Kagome lattices
- Synthetic Dimensions with Magnetic Fields and Local Interactions in Photonic Lattices
- Observation of a nonradiative flat band for spoof surface plasmons in a metallic Lieb lattice
- New class of flat-band models on tetragonal and hexagonal lattices: Gapped versus crossing flat bands
- Magnetic Response Functions in Landau Levels
- Fragile topology in line-graph lattices with two, three, or four gapped flat bands
- Landau levels, response functions and magnetic oscillations from a generalized Onsager relation
- No-go theorem for topological insulators and sure-fire recipe for Chern insulators
- Landau Levels in Strained Optical Lattices
- Artificial magnetic field for synthetic quantum matter without dynamical modulation
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- General construction of flat bands with and without band crossings based on wave function singularity
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- Fractal-like photonic lattices and localized states arising from singular and nonsingular flatbands
- Berry Phase and Topology in Ultrastrongly Coupled Quantum Light-Matter Systems
- Flat bands with band crossings enforced by symmetry representation
- Landau Levels of the Euler Class Topology
- Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence
- Unconventional gapless semiconductor in an extended martini lattice in covalent honeycomb materials