Generalized Variable Range Hopping Near Two-Dimensional Metal-Insulator Transitions

In an attempt to understand quantitatively the remarkable discoveries of metal-insulator transitions in two-dimensional systems, we generalize Mott's variable range hopping theory to the situation with strong Coulomb interaction. In our formulation, the Gaussian form is adopted into the expression of the hopping probability, and the effect of Coulomb gap is also considered. After taking account of the newly proposed scaling consideration, we produce the dynamical and localization length exponents, which are consistent with the experiments. We then clarify the physical content of our formulation and explain the universality of the localization length exponent suggested by a series of experiments. We also discuss the general scaling function of both temperature and electrical field on the insulating side of the transition.