An electronic avalanche model for metal–insulator transition in two dimensional electron gas

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In this paper, we present an electronic avalanche model for the transport of electrons in the disordered two-dimensional (2D) electron gas which has the potential to describe the 2D metal–insulator transition (MIT) in the zero electron–electron interaction limit. The disorder is considered to be uncorrelated-Coulomb noise with a uniform distribution. In this model we sub-divide the system to some virtual cells each of which has a linear size of the order of phase coherence length of the system. Using Thomas-Fermi-Dirac theory we propose some simple energy functions for the cells and using the thermodynamics of 2DEG we develop some rules for the charge transfer between the cells. A second order transition line arises from our model with some similarities with the experiments. The compressibility of the system also diverges on this line. We characterize this (disorder-driven) phase transition which is between the non-percolating phase and the percolating phase (in which the system shows metallic behavior) and obtain some geometrical critical exponents. The fractal dimension of the exterior frontier of the electronic avalanches on the transition line is compatible with the percolation theory, whereas the other exponents are different. The exponents are robust against disorder in the low disordered 2DEGs and change considerably in the high disordered ones.