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 neighbouring Landau levels. 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 $\hbar\omega_c/a_L$ ($a_L$ is the magnetic length). The sensitivity of the gap reduction is illustrated using tilted and multiple step barriers and finite stripe configurations.