Percolation-type description of the metal-insulator transition in two dimensions

A simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, is introduced [Y. Meir, Phys. Rev. Lett. 83 (1999) 3506] in order to describe the observed "metal-insulator transition" in two dimensions. Here, based upon that model, a two-species-percolation scaling theory is introduced and compared to the experimental data. It is shown that many features of the experiments, such as the exponential dependence of the resistance on temperature on the metallic side, the linear dependence of the exponent on density, the e²/h scale of the critical resistance, the quenching of the metallic phase by a parallel magnetic field and the non-monotonic dependence of the critical density on a perpendicular magnetic field, can be naturally explained by the model. Moreover, details such as the non-monotonic dependence of the resistance on temperature or the inflection point of the resistance vs. parallel magnetic field are also a natural consequence of the theory. The calculated parallel field dependence of the critical density agrees excellently with experiments, and is used to deduce an experimental value of the confining energy in the vertical direction.