Composite fermions in a long-range random magnetic field: Quantum Hall effect versus Shubnikov-de Haas oscillations

TL;DR

This paper investigates how composite fermions in a random magnetic field exhibit a transition from enhanced conductivity to localization, affecting quantum Hall and Shubnikov-de Haas oscillations.

Contribution

It provides a detailed analysis of transport phenomena in composite fermions under strong magnetic field fluctuations, highlighting the role of localization.

Findings

Percolation influences conductivity at large magnetic fluctuations.

Increasing mean magnetic field causes a sharp decrease in conductivity.

Quantum localization dominates the behavior of composite fermions away from half-filling.

Abstract

We study transport in a smooth random magnetic field, with emphasis on composite fermions (CF) near half-filling of the Landau level. When either the amplitude of the magnetic field fluctuations or its mean value $\bar B$ is large enough, the transport is of percolating nature. While at $\bar{B}=0$ the percolation effects enhance the conductivity $\sigma_{xx}$, increasing $\bar B$ (which corresponds to moving away from half-filling for the CF problem) leads to a sharp falloff of $\sigma_{xx}$ and, consequently, to the quantum localization of CFs. We demonstrate that the localization is a crucial factor in the interplay between the Shubnikov-de Haas and quantum Hall oscillations, and point out that the latter are dominant in the CF metal.