I am trying to understand the hall effects and have a few problems with them.
So let's consider the classical Hall effect. We know that we consider a sample, where the electrons flow, we apply the perpendicular magnetic field, and the electron's motion is curved so they reach the sample's edge. There appears a "new" electric field.
On the other hand, the quantum Hall effect sometimes showed that electrons move in a closed circular orbit, but not in the edge where they can go through "skipping orbits".
So my question is, why in classical hall effect the electrons teachers the sample's edge and don't just move in a circle? What is more, do they move also along the edge like in the quantum hall effect?