Hyperfine interaction induced critical exponents in the quantum Hall effect

TL;DR

This paper investigates how hyperfine interactions with nuclear spins influence the localization-delocalization transition in quantum Hall systems, revealing two distinct critical exponents for quantum and classical percolation.

Contribution

It introduces a model incorporating nuclear spin effects into quantum Hall transitions, identifying separate critical exponents for quantum and classical regimes.

Findings

Identification of two critical exponents for quantum and classical percolation.

Demonstration of the transition from 2D extended states to 1D critical states.

Analysis of nuclear polarization as an additional confining parameter.

Abstract

We study localization-delocalization transition in quantum Hall systems with a random field of nuclear spins acting on two-dimensional (2d) electron spins via hyperfine contact (Fermi) interaction. We use Chalker-Coddington network model, which corresponds to the projection onto the lowest Landau level. The inhomogeneous nuclear polarization acts on the electrons as an additional confining potential, and, therefore, introduces additional parameter $p$ (the probability to find a polarized nucleus in the vicinity of a saddle point of random potential) responsible for the change from quantum to classical behavior. In this manner we obtain two critical exponents corresponding to quantum and classical percolation. We also study how the 2d extended state develops into the one-dimensional (1d) critical state.