The Hall Effect from a classical to a quantistic description and its applications in metrology

Among one of the most important phenomena of modern physics stands out the Hall effect. We will explain the physical essence of this effect by starting with the study of the physical grounds of the classical Hall effect which is a famous example of classical electrodynamics of charged particles at work. We will then move to a quantistic description and show that the fermionic nature of the electrons in a two-dimensional electron gas system is responsible for the quantum Hall effect. We will go through the main properties of the integer quantum Hall effect in which the dependence of the Hall resistance on the magnetic field exhibits quantized plateaux at integer levels. In conclusion we will present one of the most relevant applications of the quantum Hall effect in the field of metrology focusing our attention on how the stability and reproducibility of the quantum Hall resistance open the way to more accurate resistance standards and to high precision measurements of the fine-structure constant.