Landau quantization of multilayer graphene on a Haldane sphere

Abstract

We consider the problem of multilayer graphene on a Haldane sphere and determine the Landau level spectrum for this family of systems. This serves as a generalization of the Landau quantization problem of ordinary non-relativistic Haldane sphere and spherical graphene, or Dirac-like particles on a sphere. The Hamiltonian is diagonalized in a concise algebraic fashion exploiting two mutually commuting SU(2) algebras of the problem. Additionally, using exact wave functions we demonstrate computation of Haldane pseudopotentials in the second Landau level. These exact solutions add to the current toolkits of the numerical studies on fractional quantum Hall effects in systems of graphite multilayers.

arXiv comment6 pages, 1 figure

References in corpus (21)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• The electronic properties of bilayer graphene
• Quantum Hall Physics - hierarchies and CFT techniques
• Synthetic Landau levels for photons
• Tunable Fractional Quantum Hall Phases in Bilayer Graphene
• Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene
• Lectures on the Quantum Hall Effect
• Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Integer Quantum Hall Effect in Trilayer Graphene
• A Stable Pfaffian State in Bilayer Graphene
• Landau Level Quantization on the Sphere
• Topological Phases in the Zeroth Landau Level of Bilayer Graphene
• Robust fractional quantum Hall effect and composite fermions in the $N=2$ Landau level in bilayer graphene
• Interacting surface states of three-dimensional topological insulators
• Anomalous Quantum Hall Effect on Sphere
• Landau level quantization of Dirac electrons on the sphere
• Formulation of the Relativistic Quantum Hall Effect and "Parity Anomaly"
• Landau level quantization for massless Dirac fermions in the spherical geometry: graphene fractional quantum Hall effect on the Haldane sphere

Cited by in corpus (7)

• Dual Haldane sphere and quantized band geometry in chiral multifold fermions
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Band geometry from position-momentum duality at topological band crossings
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• Geometric semimetals and their simulation in synthetic matter
• Time-reversal odd transport in bilayer graphene: Hall conductivity and Hall viscosity