The **key difference** between Hall effect and quantum Hall effect is that the **Hall effect mainly occurs on semiconductors, whereas the quantum Hall effect takes place mainly in metals. **

Hall effect refers to the generation of an electric potential perpendicular to both an electric current flowing along a conducting material and an external magnetic field applied at right angles to the current upon application of the magnetic field. This effect was observed in 1879 by Edwin Hall. The quantum Hall effect was discovered later, as a derivation of the Hall effect.

### CONTENTS

1. Overview and Key Difference

2. What is Hall Effect

3. What is Quantum Hall Effect

4. Side by Side Comparison – Hall Effect vs Quantum Hall Effect in Tabular Form

5. Summary

## What is Hall Effect?

Hall effect refers to the production of a voltage difference that is transverse to an electric current and to an applied magnetic field. Here, the voltage difference arises across an electrical conductor. The electric current is made by this electrical conductor and the magnetic field applied to it is perpendicular to the current. This effect was discovered by Edwin Hall in 1879. He also invented the Hall coefficient, which is the ratio of the induced electric field to the product of the current density and applied magnetic field. The value of this coefficient is a characteristic of the material from which the conductor is made. Therefore, the value of this coefficient depends on the type, number and properties of the charge carrier that constitute the current.

Hall effect arises due to the nature of the current in a conductor. Generally, an electric current contains the movement of many small charge carriers such as electrons, holes, ions or all three of them. When there is a magnetic field, these charges tend to experience a force called Lorentz force. When there is no such magnetic field, the charges tend to follow approximately a straight line of sight path between collisions with impurities.

Furthermore, when a magnetic field is applied perpendicularly, the path of the charges between collisions tend to curve; thus, moving charges accumulate on one face of the material, leaving equal and opposite charges exposed on the other face. This process results in an asymmetric distribution of charge density across the Hall element that arises from the force that is perpendicular to both the line of sight path and the applied magnetic field. The separation of these charges establishes an electric field. This is called the Hall effect.

## What is Quantum Hall Effect?

Quantum Hall effect is a quantum mechanical concept that occurs in a 2D electron system that is subjected to a low temperature and a strong magnetic field. Here, the “Hall conductance” undergoes quantum Hall transitions to take on the quantized values at a certain level. The mathematical expression for quantum hall effect is as follows:

Hall conductance = I_{channel}/V_{Hall} = v.e^{2}/h

I_{channel} is the channel current, V_{Hall} is the Hall voltage, e is the elementary charge, h is Plank’s constant and v is a prefactor called the filling factor that is either an integer value or a fractional value. Therefore, we can identify that the quantum hall effect is the integer of fractional quantum Hall effect depending on whether “v” is an integer or fraction, respectively.

The integer quantum Hall effect has a specific feature, that is, the persistence of the quantization as the electron density varies. Here, the electron density remains constant when the Fermi level is in a clean spectral gap; thus, this situation corresponds to one where the fermi level is an energy with a finite density of states, though these states are localized. When considering the fractional quantum Hall effect, it is more complicated because its existence relies fundamentally upon the electron-electron interactions.

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

The key difference between Hall effect and quantum Hall effect is that the Hall effect mainly occurs on semiconductors, whereas the quantum Hall effect takes place mainly in metals. Another important difference between Hall effect and quantum Hall effect is that Hall effect occurs where there is a weak magnetic field and medium temperatures while Quantum Hall effect requires stronger magnetic fields and much lower temperatures.

Below infographic summarizes the differences between Hall effect and quantum Hall effect.

## Summary – Hall Effect vs Quantum Hall Effect

The quantum Hall effect is derived from the classical Hall effect. The key difference between Hall effect and quantum Hall effect is that the Hall effect mainly occurs on semiconductors, whereas the quantum Hall effect takes place mainly in metals.

##### Reference:

1. Hall Effect. (n.d.). Retrieved September 01, 2020, Available here.

##### Image Courtesy:

1. “Hall effect” By Peo – Own work (CC BY-SA 3.0) via Commons Wikimedia

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