Hamiltonian for the spin quantum hall effect solution and derivation based on an SU (2) Gauge Field

摘要

A Hamiltonian to describe a spin quantum Hall effect with two types of spin-orbit coupling is introduced and the eigenfunctions and eigenvalues are obtained for it. It is shown that this Hamiltonian also results by gauging a kinetic energy Hamiltonian by an SU (2) gauge field. The Berry phase is obtained from the model wavefunction for the model and used to define a filling factor. This allows for the calculation of the spin Hall conductivity.