Phenomenological Model for the metal-insulator transition in two dimensions

Abstract

The resistivity measured in two-dimensional MOSFET geometry is modeled by considering that the resistivity is a function of the temperature and the areal density of charges (electrons or holes). The logistical differential equation is proposed for the behaviour of the resistivity as a function of temperature, so that the two phases are obtained in a natural manner. At low temperatures, the Drude model behaviour is assumed for the resistivity as a function of density. Two characteristics then follow in a natural manner: The existance of a characteristic temperature for resistivity as a function of temperature, and the symmetry relationship. If the magnetic field is incorporated into the Drude model, reasonable results are obtained for the qualititive behaviour of resistivity for weak fields.