Robustness of real-space topology in moiré systems
arXiv:2507.00130 · doi:10.1103/szqp-wp6h
Abstract
The appearance of fractional Chern insulators in moiré systems can be rationalized by the presence of a fictitious magnetic field associated with the spatial texture of layer-resolved electronic wavefunctions. Here, we present a systematic study of real-space topology and the associated fictitious magnetic fields in moiré systems. We first show that at the level of individual Bloch wavefunctions, the real-space Chern number, akin to a Pontryagin index, is a fragile marker. It generically vanishes except for specific limits where the Bloch functions exhibit fine-tuned zeroes within the unit cell, such as the chiral limit of twisted bilayer graphene (TBG) or the adiabatic regime of twisted homobilayer transition metal dichalcogenides (TMD). We then show that these limitations do not apply to textures associated with ensembles of Bloch wavefunctions, such as entire bands or the ensemble of states at a given energy. The Chern number of these textures defines a robust topological index protected by a spectral gap. We find that symmetries constrain it to be nonzero for both twisted TMDs and TBG across all twist angles and levels of corrugation, implying experimental signatures in scanning tunneling microscopy measurements. By projection to the band ensemble texture, a single-component Hamiltonian under fictitious magnetic field emerges in a broad regime, enabling a direct comparison of multicomponent bands to Landau-level wavefunctions. We also study real-space topology within the topological heavy fermion model of TBG, finding that the real-space topological features are supported only by the light c-electrons.
arXiv commentPublished version
References in corpus (95)
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- Moire bands in twisted double-layer graphene
- Tuning superconductivity in twisted bilayer graphene
- Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Magic continuum in twisted bilayer WSe2
- Magic Angle Spectroscopy
- Origin of Magic Angles in Twisted Bilayer Graphene
- Topological insulators in twisted transition metal dichalcogenide homobilayers
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Observation of Fractionally Quantized Anomalous Hall Effect
- Imaging Electronic Correlations in Twisted Bilayer Graphene near the Magic Angle
- Fractional quantum Hall effect in the absence of Landau levels
- Spectroscopic signatures of many-body correlations in magic angle twisted bilayer graphene
- Fractional Chern Insulator
- Topological Hall effect and Berry phase in magnetic nanostructures
- Fractional Chern insulators in magic-angle twisted bilayer graphene
- Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
- Integer and fractional Chern insulators in twisted bilayer MoTe2
- Untying the insulating and superconducting orders in magic-angle graphene
- Topological Flat Band Models and Fractional Chern Insulators
- Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
- All "Magic Angles" Are "Stable" Topological
- Electric field tunable unconventional superconductivity in alternating twist magic-angle trilayer graphene
- Cascade of electronic transitions in magic-angle twisted bilayer graphene
- Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene
- Decoupling superconductivity and correlated insulators in twisted bilayer graphene
- Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
- Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
- 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
- Nematicity and Competing Orders in Superconducting Magic-Angle Graphene
- Superconductivity without insulating states in twisted bilayer graphene stabilized by monolayer WSe
- Strong coupling phases of partially filled twisted bilayer graphene narrow bands
- Band Structure of Twisted Bilayer Graphene: Emergent Symmetries, Commensurate Approximants and Wannier Obstructions
- Quantum Criticality in Twisted Transition Metal Dichalcogenides
- Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
- Band geometry of fractional topological insulators
- Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
- MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
- Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
- Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening
- Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
- Exact Landau Level Description of Geometry and Interaction in a Flatband
- Entropic evidence for a Pomeranchuk effect in magic angle graphene
- Superconductivity in twisted bilayer WSe
- Twisted bilayer graphene. II. Stable symmetry anomaly
- Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet
- Quantum textures of the many-body wavefunctions in magic-angle graphene
- Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
- Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe
- Signatures of Chiral Superconductivity in Rhombohedral Graphene
- Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors
- Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
- Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
- Mapping twist-tuned multiband topology in bilayer WSe
- Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
- Polarization-driven band topology evolution in twisted MoTe and WSe
- Imaging inter-valley coherent order in magic-angle twisted trilayer graphene
- Superconductivity and quantized anomalous Hall in rhombohedral graphene
- Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
- Berry Curvature and Quantum Metric in -band systems -- an Eigenprojector Approach
- Heavy fermion representation for twisted bilayer graphene systems
- Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators
- Quantum Metric Induced Phases in Moiré Materials
- Non-Abelian fractionalization in topological minibands
- Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
- Ideal Chern bands are Landau levels in curved space
- Spectroscopy of Twisted Bilayer Graphene Correlated Insulators
- Theory of tunable flux lattices in the homobilayer moiré of twisted and uniformly strained transition metal dichalcogenides
- Dynamical correlations and order in magic-angle twisted bilayer graphene
- Non-Abelian Fractional Quantum Anomalous Hall States and First Landau Level Physics in Second Moiré Band of Twisted Bilayer MoTe2
- Topological exact flat bands in two dimensional materials under periodic strain
- Multiple Chern bands in twisted MoTe and possible non-Abelian states
- Detecting symmetry breaking in magic angle graphene using scanning tunneling microscopy
- Higher Landau-Level Analogs and Signatures of Non-Abelian States in Twisted Bilayer MoTe
- Adiabatic Approximation and Aharonov-Casher Bands in Twisted Homobilayer TMDs
- Magic-Angle Twisted Symmetric Trilayer Graphene as Topological Heavy Fermion Problem
- Kondo Phase in Twisted Bilayer Graphene -- A Unified Theory for Distinct Experiments
- TBG as Topological Heavy Fermion: II. Analytical approximations of the model parameters
- Weak coupling theory of topological Hall effect
- Topological Hall effect from strong to weak coupling
- Interplay of electronic crystals with integer and fractional Chern insulators in moiré pentalayer graphene
- Theory of Generalized Landau Levels and Implication for non-Abelian States
- Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe
- Higher vortexability: zero field realization of higher Landau levels
- Fractional Chern Insulators in Bands with Zero Berry Curvature
- Visualizing the microscopic origins of topology in twisted molybdenum ditelluride
- Nested-sphere description of the N-level Chern number and the generalized Bloch hypersphere
- Experimental signature of layer skyrmions and implications for band topology in twisted WSe2 bilayers
- Twisted-bilayer FeSe and the Fe-based superlattices
- Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
- Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
- Broken Symmetry in Ideal Chern Bands
- Fractional Chern insulator states in an isolated flat band of zero Chern number