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

We study transport in a smooth random magnetic field, with emphasis on composite fermions (CFs) near half-filling of the Landau level. When either the amplitude of the magnetic field fluctuations or its mean value (B) over bar is large enough, the transport is percolating in nature. While at (B) over bar = 0 the percolation enhances the conductivity sigma(xx), increasing (B) over bar leads to a sharp falloff of sigma(xx) and, consequently, to the quantum localization of CFs. We show that the localization is a crucial factor in the interplay between the Shubnikov-de Haas and quantum Hall oscillations and that the latter are dominant in the CF metal.