ELECTRON ON A LATTICE IN A MAGNETIC-FIELD

I consider an electron on a 2D lattice of arbitrary short-range scatterers in magnetic field. I accurately reduce its Schroedinger equation to an explicit Hermitian matrix. If the number phi of magnetic-flux quanta per site is less than one, then similar or equal to (1 - phi)-th fraction of all states condenses into narrow high-density-of-states bands in the vicinity of Landau levels. Point scatterers shrink these bands into infinitely degenerate Landau levels. The states in the bands have high mobility in two and are extended in three dimensions. Magnetoresistance oscillates with magnetic field and may be non-monotonic with temperature and impurity concentration.