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First Order Metal-Insulator Transition in Two-dimensional Disordered Systems

In the absence of magnetic field or spin-orbit coupling the one-parameter scaling theory predicts localization of all states in two-dimensional (2D) disordered systems, for any amount of disorder. However, a 2D metallic phase has been recently reported in high mobility Si-MOS and GaAs-based materials without magnetic field. We study numerically a recently proposed 2D model which consists of a compactly coupled pure-random plane structure. This allows to obtain exactly a continuum of one-dimensional ballistic extended states which can lead to a marginal metallic phase of finite conductivity $σ_{0}=2e^2/h$, in a wide energy range whose boundaries define the mobility edges of a first-order metal-insulator transition. We present numerical diagonalization results and the conductivity of the system in perpendicular magnetic field, which verify the above analytical predictions. The model is also discussed in connection to recent experiments.