# What is the Hall Effect?

A circuit is formed here with a conductor and a battery. The battery closes the circuit and provides the voltage to push the electrons through the conductor. This generates a current. Now let’s place that conductor in a magnetic field and see what happens. The electrons are pushed to the side! This effect is called the Hall Effect (HE). The HE is due to the Lorentz force, which appears when charged particles move through a magnetic field. (The full law describing this includes the influence of electric fields as well). Electrons are pushed to one side of the conductor and leaves that side more negatively charged. The other side is left more positively charged. Since there is a charge difference, an electric field is generated in the conductor pointing from the positive side to the negative side.

#### Left and Right Hand Rules

If you want to figure out which way the particles are pushed, you can use the left hand rule (LHR). First, make a gun with your left hand, but point the middle finger out to your right. The index finger points in the direction of the magnetic field (which always points from north to south); the middle finger, the current (direction of particle motion); the thumb, the force. An easy way to remember which finger is for which component, notice that from top to bottom (thumb to middle finger), it spells out FBI. Now orient your fingers to match the picture above and see what you get.

Notice how the force you got is in the opposite direction. Try the same thing with your right hand and you will find that your thumb points in the correct direction. This is the right hand rule (RHR). So which one should you use? There are two ways of remembering which method to use:

• Use LHR for positive charges and RHR for negative charges, or
• Use either LHR or RHR, as long as you remember that for LHR, flip the force for negative charges; for RHR, flip the force for positive charges.

## Quantum Hall Effect (QHE)

The QHE is essentially the same thing but with a twist. In a material, there are many electrons bound by regions called orbitals. Electrons constantly move around in these orbitals. The QHE is exhibited in some materials when they are cooled to around 4 K (-452 °F or -269 °C) and put through magnetic fields at around 10 teslas (10,000 stronger than a refrigerator magnet). The electrons in the bulk of the material do not conduct electricity and are free to orbit around their atoms’ nuclei. The electrons on the edges, though, don’t get to finish their orbits. They bounce off the edges and try orbiting again. All of these continuous bounces lets us say that the electrons are effectively moving along the edges. In other words, a current is generated. The QHE is the principle behind topological insulators. It should be noted that one of the main reasons that it’s called the quantum Hall Effect is because the Hall resistance in the material increases in a stepwise, quantifiable fashion after a sufficient magnetic field is applied.

## Spin Hall Effect (SHE)

This is a spin on the classical HE. The Spin Hall Effect ideally occurs in 2D materials (atom thick materials), but SHE can also be seen in thicker materials on their outer edges. When a charge imbalance forms in the materials due to the HE, an electric field forms. In the presence of an electric field, the electrons are pushed to opposite sides dictated by their spin. This generates a “spin current” which moves perpendicular to the electric current. Unlike the QHE, this occurs without an external magnetic field. Applying one would actually negate the effect, since it would cause the electrons to precess instead of move towards opposite sides from each other. The SHE could have possible applications in the field of spintronics, in which electron spin is used for computing.