Two dimensional magnetic Schrodinger operators: Width of mini bands in thetight binding approximation

The spectral properties of two dimensional magnetic Schrodinger operators a re studied. It is shown in the tight-binding limit that when a nonzero cons tant magnetic field is perturbed by an infinite number of magnetic and scal ar "wells", the essential spectrum continues to have gaps and moreover, it can be nonempty in be tween the Landau levels and is localized near the one well Hamiltonian eigenvalues which develop into mini-bands whose width is believed to be optimally controlled.