Short-range impurity in the vicinity of a saddle point and the levitation of the two-dimensional delocalized states in a magnetic field

The effect of a short-range impurity on the transmission through a saddle-point potential for an electron, moving in a strong magnetic field, is studied. It is demonstrated that for a random position of an impurity and random sign of its potential, the impurity-induced mixing of the Landau levels diminishes on average the transmission coefficient. This results in an upward shift (levitation) of the energy position of the delocalized state in a smooth potential. The magnitude of the shift is estimated. It increases with decreasing magnetic field B as B^-4. {} 1996 The American Physical Society.