Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The -Jellium model
arXiv:2509.15300 · doi:10.1103/5w7g-j4cf
Abstract
Recent experiments on multilayer graphene systems have rekindled interest in electronic crystal phases in two dimensions -- but now for phases enriched by non-trivial quantum geometry. In this work, we introduce a simple continuum model with tunable Berry curvature distribution and total flux, enabling systematic study of crystallization in geometrically nontrivial bands. In the noninteracting limit, the addition of a C6-symmetric periodic potential yields a rich phase diagram, for which we provide several analytical insights. Notably, we derive a general formula for the Chern number in the weak-potential regime that is broadly applicable to single-band projected models. Removing the periodic potential and treating Coulomb interactions self-consistently at the Hartree-Fock level, the resulting phase diagrams host a variety of crystalline states, including anomalous Hall crystals, halo Wigner crystals in which localized electrons spontaneously acquire orbital angular momentum leading to depleted electron occupation at the zone center, and a novel halo anomalous Hall crystal that combines these properties with a finite Chern number. We identify why these phases are energetically favorable through analytical and energetic considerations. Our results provide insight into the interplay between crystallization and band geometry, while also offering a simple toy model amenable to numerical methods beyond mean-field.
22 + 16 pages, 9 + 4 figures
References in corpus (38)
- Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
- Observation of Wigner crystal of electrons in a monolayer semiconductor
- Exact Landau Level Description of Geometry and Interaction in a Flatband
- Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands
- Quantum cascade of new correlated phases in trigonally warped bilayer graphene
- Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
- Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
- Signatures of Chiral Superconductivity in Rhombohedral Graphene
- Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
- Direct observation of a magnetic field-induced Wigner crystal
- Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
- Competing correlated states around the zero field Wigner crystallization transition of electrons in two-dimensions
- Quantum geometry in condensed matter
- Observation of Spontaneous Ferromagnetism in a Two-Dimensional Electron System
- Quantum Metric Induced Phases in Moiré Materials
- Stability of Anomalous Hall Crystals in multilayer rhombohedral graphene
- Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
- Parent Berry curvature and the ideal anomalous Hall crystal
- Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid
- Sublattice structure and topology in spontaneously crystallized electronic states
- Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
- Topological electronic crystals in twisted bilayer-trilayer graphene
- Self-doping instability of the Wigner-Mott insulator
- Theory of Generalized Landau Levels and Implication for non-Abelian States
- Gauge-invariant projector calculus for quantum state geometry and applications to observables in crystals
- Ground state phases of the two-dimension electron gas with a unified variational approach
- Extended quantum anomalous Hall effect in moiré structures: phase transitions and transport
- Computing observables without eigenstates: applications to Bloch Hamiltonians
- Phonons in Electron Crystals with Berry Curvature
- Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid
- -Jellium Model for the Anomalous Hall Crystal
- Evidence of zero-field Wigner solids in ultra-thin films of cadmium arsenide
- Effective field theory of Berry Fermi liquid from the coadjoint orbit method
- Berry Phase Dynamics of Sliding Electron Crystals
- Chiral Wigner crystal phases induced by Berry curvature
- Critical gate distance for Wigner crystallization in the two-dimensional electron gas
- Dynamical matrix of two-dimensional electron crystals
- Quantum Monte Carlo study of the quasiparticle effective mass of the two-dimensional uniform electron liquid