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

A. D. Mirlin·D. G. Polyakov·P. Woelfle
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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 $σ_{xx}$, increasing $\bar B$ (which corresponds to moving away from half-filling for the CF problem) leads to a sharp falloff of $σ_{xx}$ 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.

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A. D. Mirlin, D. G. Polyakov, P. Woelfle. 1997-10-14. Composite fermions in a long-range random magnetic field: Quantum Hall effect versus Shubnikov-de Haas oscillations. https://doi.org/10.1103/physrevlett.80.2429

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