Landau level mixing and spin degeneracy in the quantum Hall effect

TL;DR

This paper investigates how Landau level mixing and spin degeneracy affect electron dynamics in the quantum Hall effect, revealing conditions for level attraction or repulsion and their implications for localization and extended states.

Contribution

It introduces a network model with random channel mixing to analyze the effects of Landau level and spin state interactions on quantum Hall phenomena, including level behavior and localization.

Findings

Level mixing causes transition from repulsion to attraction with increasing energy separation.

At low magnetic fields, Landau levels exhibit level floating behavior.

A single extended state exists with a localization exponent of approximately 1.1.

Abstract

We study dynamics of electrons in a magnetic field using a network model with two channels per link with random mixing in a random intrachannel potential; the channels represent either two Landau levels or two spin states. We consider channel mixing as function of the energy separation of the two extended states and show that its effect changes from repulsion to attraction as the energy separation increases. For two Landau levels this leads to level floating at low magnetic fields while for Zeeman split spin states we predict level attraction at high magnetic fields, accounting for ESR data. We also study random mixing of two degenerate channels, while the intrachannel potential is periodic (non-random). We find a single extended state with a localization exponent $\nu\approx 1.1$ for real scattering at nodes; the general case has also a single extended state, though the localized nature of nearby states sets in at unusually large scales.