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Quantum Hall effect (theorized 1975, observed 1978)

Quantum version of the Hall effect.

As you increase the magnetic field, you can see the Hall resistance increase, but it does so in discrete steps.

Figure 1. Hall resistance as a function of the applied magnetic field showing the Quantum Hall effect. Source. As we can see, the blue line of the Hall resistance TODO material, temperature, etc. It is unclear if this is just

Gotta understand this because the name sounds cool. Maybe also because it is used to define the fucking ampere in the 2019 redefinition of the SI base units.

At least the experiment description itself is easy to understand. The hard part is the physical theory behind.

TODO experiment video.

The effect can be separated into two modes:

Integer quantum Hall effect: easier to explain from first principles
Fractional quantum Hall effect: harder to explain from first principles
- Fractional quantum Hall effect for $ν = 1 / m$ : 1998 Nobel Prize in Physics
- Fractional quantum Hall effect for $ν \neq = 1 / m$ : one of the most important unsolved physics problems as of 2023

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