Using a variational procedure within the effective mass approximation, the ionization energies of a shallow donor in a quantum well (QW) of GaAs/Ga 1-x Al x As superlattice system under the influence of pressure with the exact dielectric function are obtained. The vanishing of ionization energy initiating Mott transition is observed within the one-electron approximation. The effects of Anderson localization using a simple model, and exchange and correlation in the Hubbard model are included in this model. It is found that the ionization energy (i) increases when well width increases for a given pressure, (ii) decreases and reaches a bulk value for a larger well width, (iii) increases with increasing external hydrostatic pressure for a given QW thickness, and (iv) the critical concentration at which the metal–insulator transition (MIT) occurs is increased when pressure is applied. It also is demonstrated that MIT is not possible in a hydrostatic pressure in a quantum well supporting scaling theory of localization. All the calculations have been carried out with finite and infinite barriers and the results are compared with available data in the literature.
Metal-insulator transition in disordered systems from the one-body density matrix
