A geometrical approach to the quantized Hall effect (for use in metrology)

A very rudimentary phenomenological model of the QHE (quantized Hall effect) is proposed. It is based on a semiclassical approximation which, although not rigid in a theoretical sense, gives some insight into the geometrical parameters involved in the QHE and, by its semiclassical character, provides an interpretation of the operators involved in the theory of the QHE. The model gives most of the observable features of the integral QHE. The influence of the finite width of the sample as well as the current and temperature dependence can be taken into account using the model. Although the model fails in fitting the fractional effect and it has to be used with great care above the critical current since no interband transitions have been taken into account, it could prove useful for the classification of samples for metrological use. For example, the expressions indicate that both the magnetic and the electrical mobility are important for classifying a sample´s quality.<>