Landau-level mixing and extended states in the quantum Hall effect

We study the energies of extended states for two coupled Landau bands within a network model as a function of Delta, the bare energy separation of extended states in the absence of level mixing. As Delta increases the energy separation of the extended states becomes less than the bare energy separation, i.e., at high-level separation, level repulsion changes into level attraction. The level attraction leads to a minimum in the energy of the lower state at a finite magnetic field, consistent with level floating at low fields. For a spin-split Landau level we predict level attraction at high magnetic fields.