Anomalous Quantum Hall Effect on Sphere

Understand

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--Schr\"odinger 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.