Anomalous Quantum Hall Effect on Sphere

Abstract

We study the anomalous quantum Hall effect exhibited by the relativistic particles living on two-sphere S^2 and submitted to a magnetic monopole. We start by establishing a direct connection between the Dirac and Landau operators through the Pauli--Schrödinger Hamiltonian H_{s}^{SP}. This will be helpful in the sense that the Dirac eigenvalues and eigenfunctions will be easily derived. In analyzing H_{s}^{SP} spectrum, we show that there is a composite fermion nature supported by the presence of two effective magnetic fields. For the lowest Landau level, we argue that the basic physics of graphene is similar to that of two-dimensional electron gas, which is in agreement with the planar limit. For the higher Landau levels, we propose a SU(N) wavefunction for different filling factors that captures all symmetries. Focusing on the graphene case, i.e. N=4, we give different configurations those allowed to recover some known results.

23 pages, clarifications, references added, misprints corrected. Version to appear in NPB

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Cited by in corpus (12)

• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• Confined Dirac Fermions in a Constant Magnetic Field
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Landau quantization of multilayer graphene on a Haldane sphere
• Landau level quantization for massless Dirac fermions in the spherical geometry: graphene fractional quantum Hall effect on the Haldane sphere
• Anomalous Quantum Hall Effect of 4D Graphene in Background Fields
• Fractional Quantum Hall States in Graphene
• Path Integral Confined Dirac Fermions in a Constant Magnetic Field
• 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
• Magnetism of Two Coupled Harmonic Oscillators
• Remarks on Fermions in a Dipole Magnetic Field