Question

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?

Answer 1

In the classical Hall effect, electrons reach the sample's edge due to the boundary of the conductor, whereas in the quantum Hall effect, electrons can move in closed orbits at the edges due to quantum mechanics. The electric force balances the magnetic force, creating the Hall emf across the conductor.

Step-by-step explanation:

Understanding the Classical Hall Effect

In the classical Hall effect, we consider the motion of free electrons in a metallic strip placed in a perpendicular magnetic field. Electrons moving from left to right experience a magnetic force that pushes them toward the bottom edge of the strip. This migration of electrons creates an excess of positive charge at the top edge, leading to an electric field directed from top to bottom. The charge accumulation continues until the electric force, Fe = qE, counterbalances the magnetic force, FB = quB, resulting in equilibrium. Consequently, a voltage known as the Hall emf, represented by &, is established across the conductor.

The reason electrons don't just move in circles but reach the sample's edge is because of the conductor's restraining boundaries, which limit the circular motion. In the quantum Hall effect, however, at very low temperatures and high magnetic fields, electrons can indeed move in closed circular orbits, particularly at the edges in what is known as edge states. The classical effect is distinguished from the quantum effect since, in the latter, electrons can move along the edge in skipping orbits due to quantum mechanics characteristics, which don't appear in the classical setting.

The classical Hall effect is essential for understanding the behavior of charge carriers and is utilized in various applications, including the determination of carrier concentration, types of carriers, and even measuring magnetic field strength. The discovery of the Hall effect by Edwin Hall has significantly impacted the way we understand and measure electrical conductance phenomena.