The 2D Metal-Insulator Transition: A percolative Monte Carlo study

We examine the metal-insulator transition (MIT) in two dimensional electronic systems (e.g. n doped GaAs heterostructures) in the presence of a long-range Coulombic random potential set up by a nearby layer of charged impurities. An iterative scheme taking into account nonlinear screening is used to obtain the inhomogeneous ``landscape'' of electron-rich and electron-depleted regions. The percolation (or not) of electron rich areas (in the regime of electronic densities $n$ where linear screening breaks down) is determined by a variant of the Hoshen Kopelman algorithm. Identifying the percolation transition as the metal-insulator transition, we calculate the critical electron density $n_{c}$ as a function of the concentration of charged impurities, the separation $d$ of the impurity layer from the electronic layer, and the thickness of the impurity rich region; the effect of correlated impurity positions is also examined. Using finite size scaling analysis, we calculate the critical exponent $\delta$ for the asymptotic scaling $\sigma \propto (n - n_{c})^{\delta}$ in the vicinity of the MIT. We acknowledge support from US-ONR and NRI-NSF.