What is the Difference Between Hall Effect and Quantum Hall Effect?

The Hall effect and the Quantum Hall effect are related phenomena, but they have distinct differences. The key differences between them are:

1. Occurrence: Hall effect mainly occurs in semiconductors, while the Quantum Hall effect takes place mainly in metals.
2. Quantization: The Quantum Hall effect is a quantized version of the Hall effect, where the Hall resistance exhibits steps that take on quantized values. These steps can have integer or fractional values, depending on the specific type of Quantum Hall effect (integer or fractional).
3. Landau Levels: The Quantum Hall effect arises from the energy bands comprising the Landau levels of electrons, which are formed when electrons move in two dimensions under the influence of a magnetic field.
4. Conductance Plateaus: In the Integer Quantum Hall Effect (IQHE), the conductance plateaus occur only at integer values of the ratio e^2/h, while in the Fractional Quantum Hall Effect (FQHE), these Hall conductance plateaus occur in rational values.

In summary, the Hall effect is a wider phenomenon that occurs in semiconductors and involves the generation of a voltage difference perpendicular to both an electric current and a magnetic field. The Quantum Hall effect, on the other hand, is a more specific and quantized version of the Hall effect that occurs mainly in metals and is characterized by the presence of quantized Hall resistance and dissipationless currents in a two-dimensional electron gas.

Comparative Table: Hall Effect vs Quantum Hall Effect

The Hall Effect and Quantum Hall Effect are related phenomena, but they have distinct differences. Here is a comparison between the two:

The Hall Effect refers to the production of a voltage difference that is transverse to an electric current in an electrical conductor when a magnetic field is applied. On the other hand, the Quantum Hall Effect is derived from the classical Hall Effect and requires stronger magnetic fields and much lower temperatures. The main difference between the two is that the conductance in the Quantum Hall Effect is quantized, while it is not in the classical Hall Effect.