Effect of Landau-level mixing for electrons in a random magnetic field

An effective Hamiltonian approach is used to study the effect of Landau-level mixing on the energy spectrum of electrons in a smooth but random magnetic field B(r) with a finite uniform component B₀. It is found that, as opposed to electrostatic disorder, the energy levels of localized electrons shift upward with a rate of order O(B₀⁻¹) when B₀ is decreased, while the extended states remain static at the same order. Therefore, there is no indication that the extended states will float out of the Fermi energy and induce a metal-insulator transition as the magnetic disorder is increased. We also find that the Zeeman term may have a significant effect on the spectral shift of low-lying Landau levels.