Quantum-interference effect on AC transport of electrons subject to long-range random magnetic fields

We numerically stud's the spatial profiles of wavefunctions and the frequency dependences of the ac conductivity sigma(omega) for two-dimensional electron systems subject to long-range random magnetic fields (RMF) with zero mean. It ib found, for a weak RMF. that amplitudes of the wavefunction are almost uniformly distributed over the system, and the ac conductivity, is described by, the Drude theory Under a strong RMF, quantum states corresponding to classical snake trajectories can be strongly localized, which implies that the quantum interference along zero magnetic field contours is crucial for understanding electron transport. In this case, the conductivity sigma(omega) rapidly increases in the frequency regime lower than a crossover frequency omega (c) and decreases linearly omega much greater than omega (c). The crossover frequency is governed the localization length of the electron eigenstate at the Fermi energy.