# What is the Quantum Hall Effect?

The quantum Hall effect is a phenomenon that occurs when an electric current is passed through a thin film of conducting material in the presence of a strong magnetic field. This effect leads to the quantization of the Hall resistivity, which means that the resistance of the material becomes quantized at specific values, known as the Hall plateaus. The quantum Hall effect is a quantum mechanical effect and can only be explained by the principles of quantum mechanics.

The Hall resistivity is given by the ratio of the voltage across the material to the current flowing through it. When a magnetic field is applied perpendicular to the thin film, the electrons in the material move in circular orbits around the magnetic field lines. This motion leads to the quantization of the energy levels of the electrons, which leads to the quantization of the Hall resistivity.

# The Discovery of the Quantum Hall Effect

The quantum Hall effect was first discovered in 1980 by Klaus von Klitzing, a German physicist, who was awarded the Nobel Prize in Physics in 1985 for his work. Von Klitzing discovered that the Hall resistivity of a thin film of gallium arsenide becomes quantized at specific values when subjected to a strong magnetic field at low temperatures. This discovery revolutionized the field of condensed matter physics and led to the development of new techniques for measuring electrical resistance.

Since then, the quantum Hall effect has been observed in many other materials, including graphene, which has led to the development of new applications and technologies. The discovery of the quantum Hall effect also paved the way for the discovery of other topological phases of matter, which have important implications for the development of quantum computers.

# Applications of the Quantum Hall Effect

The quantum Hall effect has many applications in modern technology, including in the development of precision measurement devices and quantum computers. The quantized Hall resistance is used as a standard for resistance measurements, which are important for the calibration of electronic devices, such as voltmeters and ammeters.

The quantum Hall effect is also used in the development of quantum computers, which rely on the principles of quantum mechanics to perform calculations. The quantization of the Hall resistance is an example of a topological phase of matter, which is a type of phase that is robust against perturbations. This property is important for the development of quantum computers, which require stable and robust systems for performing calculations.

# Example of the Quantum Hall Effect in Action

One example of the quantum Hall effect in action is the development of the quantum Hall effect thermometer, which is a highly accurate thermometer that is based on the principles of the quantum Hall effect. The quantum Hall effect thermometer works by measuring the Hall resistance of a thin film of material, which is proportional to the temperature of the material.

These thermometers are highly accurate and can measure temperatures with a precision of up to a few parts per million. Quantum Hall effect thermometers are used in a variety of applications, including in the calibration of other thermometers and in the monitoring of temperature-sensitive processes in industry.