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

Abstract

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 metalinsulator 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.

Flicker Noise in Two-Dimensional Electron Gas

“…In this section we briefly describe the method that was developed in [3,24]. In this dynamical model, percolation of electrons with avalanche dynamics was proposed as the source for MIT of a two-dimensional electron gas at zero magnetic field.…”

“…the quantum fluctuations do not play a vital role. This approach has been proved to be very useful for the interpretation of finite-size power-law conductivity of 2DEG [39], the self-averaging [40] and percolation prescription of 2DEG [41], each of which considers the linear size ∆L ∼ ζ φ as an important spatial scale [3].…”

“…Two-dimensional electron gas (2DEG) has been a challenging topic in condensed matter physics for many years. The challenging behaviors of 2DEG, like the metalinsulator transition (MIT) and 1/f noise, have put it at the center of a long-running debates [1][2][3][4]. According to one-parameter scaling theory [1], in the absence of spin interaction and scattering no MIT is expected in 2D, the fact that was violated by the experiments of Kravchenko [5].…”

“…According to one-parameter scaling theory [1], in the absence of spin interaction and scattering no MIT is expected in 2D, the fact that was violated by the experiments of Kravchenko [5]. Despite of the huge attempts for explanation of this MIT [6,7], it has been remaining as a big mystery in the condensed matter physics, for a good review see [3]. 1 f (flicker) noise in 2DEG is another big mystery low-dimensional condensed matter whose source is not known yet.…”

“…Here we add another possibility to the list, which is based on the recent study on 2DEG which concentrates on the electronic coherence length (CL) [3]. The ingredients of this approach is discretizing the system (in the presence of charged disorder, and zero-interaction limit) according to temperature dependent CL and using the Thomas-Fermi-Dirac approximation for the quantum system for length scales much smaller than CL, and semi-classical Metropolis approach for length scale much larger than CL.…”