Non-Achievability of Metal--Insulator Transition in Two-Dimensional Systems

We present a simple demonstration of the nonfeasibility of metal-insulator transition in an exactly two-dimensional (2D) system. The Hartree--Fock potential in the 3D system is suitably modified and presented for the 2D case. The many body effects are included in the screening function, and binding energies of a donor are obtained as a function of impurity concentration so as to find out the possible way leading metal-insulator transition in the 2D system. While solving for the binding energy for a shallow donor in an isolated well of a GaAs/Ga_1-x Al_s As superlattice system within the effective mass approximation, it leads to unphysical results for higher concentrations. It shows that the phase transition, the bound electron entering into the conduction band whereby _min= 0, is not possible beyond this concentration. The results suggest that a phase transition is impossible in 2D systems, supporting the scaling theory of localization. The results are compared with the existing data available and discussed in the light of existing literature.