The integer quantum Hall effect

We see that the group velocity − →vk = 1 ~ ∂ k ∂k ŷ has the opposite sign on the two edges of the sample.This means that in the ground state there are edge currents of opposite sign flowing in the sample. The semi-classical interpretation of these currents is that they represent ’skipping orbits’ in which the circular cyclotron motion is interrupted by collisions with the walls at the edges as illustrated in fig.2.