Continuous Localisation–Delocalisation Transition at Intermediate Electron Densities

Abstract

We find in 2D electron layers in quantum transistors that the interplay between the electron correlations and their interactions with defects in the semiconductor substrate generates a continuous localisation–delocalisation transition for intermediate electron densities (5 ≲ r_s ≲ 9). We distinguish this transition from the discontinuous metal–insulator transition which is observed at lower electron densities (r_s ≳ 10). The approach we use is based on the behaviour of electrons at low densities. We take into account the interactions between electrons and also their interactions with disorder. We determine a zero temperature phase diagram of localised and delocalised states as a function of electron and impurity densities. The phase boundary of the continuous transition is determined by the localisation length of the electrons.