Hall conductivity of minibands lying at the wings of Landau levels

A semiclassical method is suggested for the description of the energy spectrum of a two-dimensional magnetic Bloch electron in a periodic potential not necessarily smaller than the cyclotron energy. With this method, each Landau band is described as a spectrum of the appropriate one-dimensional Harper-type operator and represents a series of minibands, with the near-edge minibands being flat within the exponential accuracy. It is shown that, irrespective of the potential shape, all these minibands do not contribute to the quantized Hall conductivity.