LANDAU LEVEL GAP REDUCTION AT ABRUPT EDGES

For an electron localized near a finite rectangular step potential under strong magnetic field we found a profound local reduction of the gap between neighboring Landau levels.1,2 We investigate under what conditions the effect persists when the barrier gets smoother. The conclusion is that to get a substantial gap reduction the barrier gradient has to be larger than ħwc/aL (aL is the magnetic length). The sensitivity of the gap reduction is illustrated using tilted and multiple step barriers and finite stripe configurations.