Spin-flip scattering at quantum Hall transition

TL;DR

This paper develops a generalized network model to analyze how nuclear spin-induced spin-flip scattering influences the quantum Hall transition, revealing the emergence of metallic phases between traditional insulating states.

Contribution

It introduces an exact analytical expression for transmission with spin-flip effects and demonstrates the creation of metallic phases around the quantum Hall transition.

Findings

Spin-flip scattering induces metallic states near the transition.

Traditional insulating phases are separated by metallic phases.

Analytical expression for transmission coefficient with spin-flip effects.

Abstract

We formulate a generalized Chalker--Coddington network model that describes the effect of nuclear spins on the two-dimensional electron gas in the quantum Hall regime. We find exact analytical expression for the transmission coefficient of a charged particle through a saddle point potential in presence of perpendicular magnetic field that takes into account spin-flip processes. Spin-flip scattering creates a metallic state in a finite range around the critical energy of quantum Hall transition. As a result we find that the usual insulating phases with Hall conductance $\sigma_{xy}=0, 1, 2$ are separated by novel metallic phases.