Landau level quantization for massless Dirac fermions in the spherical geometry: graphene fractional quantum Hall effect on the Haldane sphere

Abstract

We derive the single-particle eigenenergies and eigenfunctions for massless Dirac fermions confined to the surface of a sphere in the presence of a magnetic monopole, i.e., we solve the Landau level problem for electrons in graphene on the Haldane sphere. With the single-particle eigenfunctions and eigenenergies we calculate the Haldane pseudopotentials for the Coulomb interaction in the second Landau level and calculate the effective pseudopotentials characterizing an effective Landau level mixing Hamiltonian entirely in the spherical geometry to be used in theoretical studies of the fractional quantum Hall effect in graphene. Our treatment is analogous to the formalism in the planar geometry and reduces to the planar results in the thermodynamic limit.

arXiv comment14 pages, 9 figures; v2 is published version with additional references and an additional section "Many-body exact diagonalization" with 2 new figures

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Cited by in corpus (6)

• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Landau quantization of multilayer graphene on a Haldane sphere
• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Particle-Hole Mirror Symmetries around the Half-Filled Shell: The Quantum Numbers and Algebraic Structure of Composite Fermions