Mott constant in two-dimensional metal–insulator transition

The recent developments of scaling theory of metal–insulator transition in two dimensions are elicited in a good manner. Metal–Insulator transition using exact two-dimensional dielectric function is investigated for a shallow donor in an isolated well of GaAs/Ga1−xAlsAs superlattice system within the effective mass approximation. Vanishing of the donor ionization energy as a function of well width and the donor concentration suggests that the phase transition is not possible even below a well width of 10 Å supporting the scaling theory of localization. The effects of Anderson localization, exchange and correlation in the Hubbard model are included in a simple way. The relationship between the present model and the Mott criterion in terms of Hubbard model is also brought out. A simple expression for a Mott constant in 2D, a*Nc1/2 exp (−9.86 exp(−L/a*))=0.123, where Nc is the critical concentration per area, is derived. The critical concentration is enhanced when a random distribution of impurities is considered. The limiting behaviour of well width for a quantum 2D is brought out. The results are compared with the existing data available.