Flat bands on spherical surface: from Landau levels to giant-quantum-number orbitals

Abstract

Flat bands result in a divergent density of states and high sensitivity to interactions in physical systems. While such bands are well known in systems under magnetic fields, their realization and behavior in zero-field settings remain largely unexplored. Here we compare the behavior of electrons confined to a single flat band on the surface of a sphere to those in flat bands under a magnetic field. The zero-field flat band exhibits an additional C(2) symmetry, which causes electrons to symmetrically cluster on opposite sides of the sphere's center when a trapping potential is introduced, resulting in a unique form of long-range "entanglement". To explore these findings experimentally, we propose a feasible setup to explore the unique properties of zero-field flat bands on spherical substrates, offering a promising route for studying interaction-driven states in spherical geometry without external fields.

arXiv comment13 pages, 7 figures

References in corpus (29)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Tuning superconductivity in twisted bilayer graphene
• Topological Flat Band Models and Fractional Chern Insulators
• High-temperature surface superconductivity in topological flat-band systems
• Fractional Quantum Hall Physics in Topological Flat Bands
• Measurement of areas on a sphere using Fibonacci and latitude-longitude lattices
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Landau Level Mixing and the Fractional Quantum Hall Effect
• Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
• Superconducting Transitions in Flat Band Systems
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Emulating heavy fermions in twisted trilayer graphene
• Landau Level Mixing in the Perturbative Limit
• Ground state of two electrons on a sphere
• Landau level mixing in the nu=5/2 fractional quantum Hall state
• Temperature dependent magnetotransport around $\nu$= 1/2 in ZnO heterostructures
• Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect
• Composite fermion valley polarization energies: Evidence for particle-hole asymmetry
• Fractional Quantum Hall State at Filling Factor $\nu =1/4$ in Ultra-High-Quality GaAs 2D Hole Systems
• Aspects of Three-body Interactions in Generic Fractional Quantum Hall Systems and Impact of Galilean Invariance Breaking
• Molecular Kondo effect in flat-band lattices
• Development of long-range phase coherence on the Kondo lattice
• The Monte Carlo simulation of the topological quantities in FQH systems
• Two and three electrons on a sphere: A generalized Thomson problem
• Effective classical correspondence of the Mott transition
• Superlattice induced electron percolation within a single Landau level
• Robust translational invariance in topological bands against lattice potentials and disorders