Effect of spin degeneracy on scaling in the quantum Hall regime

We study the delocalization transition for spin-polarized and spin-degenerate noninteracting electrons in the lowest Landau level. We perform finite-size scaling calculations of the Thouless number for varying amounts of potential and spin-orbit scattering. For spin-polarized electrons, we obtain a one-parameter scaling function for the Thouless number that fits scaled experimental data for the longitudinal resistivity. For spin-degenerate electrons with spin-orbit scattering, the Thouless number is peaked away from the band center by an amount proportional to the strength of the spin-orbit scattering. The universality class of the delocalization transition for noninteracting spin-degenerate electrons in the quantum Hall regime is found to be the same as for spin-polarized electrons. We also study the density of states and Thouless number for the model of pure spin-orbit scattering studied by Hikami, Shirai, and Wegner [Nucl. Phys. B 408, 415 (1993)], which represents a different universality class.