Effect of spin degeneracy on scaling in the quantum Hall regime

TL;DR

This paper investigates how spin degeneracy and spin-orbit scattering influence the localization-delocalization transition in the quantum Hall regime, revealing that universality class remains consistent across different spin conditions.

Contribution

It provides a detailed finite-size scaling analysis of the Thouless number for spin-polarized and spin-degenerate electrons, identifying the effects of spin-orbit scattering on the transition.

Findings

Universal scaling function for spin-polarized electrons matches experimental data.

Spin-orbit scattering shifts the Thouless number peak away from band center.

Universality class is the same for spin-polarized and spin-degenerate electrons.

Abstract

We study the delocalization transition for spin-polarized and spin-degenerate non-interacting 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 non-interacting 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. {\bf B408}, 415 (1993)], which represents a different universality class.