Percolation transition in two dimensional electron gas: A cellular automaton model

Using the notion of phase coherence length ζϕ, a quantum cellular automaton model for two-dimensional electron gas (2DEG) is designed leading to a new type of disorder-driven electronic percolation transition. This transition is shown to be accompanied by a metal-insulator transition, as well as a singularity in the electronic compressibility. The cellular automaton model for transporting the electrons is developed in terms of the temperature (T) and the disorder strength (Δ). At the transition line some power-law behaviors emerge with critical exponents consistent with the Gaussian free field (GFF) and partly the percolation theory. Our model yields the important features of the experimental observations, e.g. the singularity in the conductivity in a critical density and also the universality (non-universality) of the metal-insulator transition (MIT) for the small (large) disorders in 2DEG. A T −Δ phase diagram of the electron gas is drawn in which in addition to the mentioned transition line, a zero-heat capacity line is also observed in which the system becomes unstable.