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 Angstrom 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 213, a*N-c(1/2) exp (-9.86 exp(-L/a*)) = 0.123, where N-c 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. (C) 2004 Elsevier B.V. All rights reserved.