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4 Scaling theory of localization In two-dimensional (2D) systems it was suggested theoretically by Abrahams and coworkers  that the ground state at zero temperature is of an insulating nature. This prediction was based on a picture of non-interacting electrons. In their paper these authors present scaling arguments indicating that the conductance G of a disordered electronic system depends on its size L in a universal way. They introduce the scaling function d ln g β(g) = , d ln L h) is the dimensionless conductance and derive asymptotic forms where g = G/(e2 /¯ for this function.
Temperature dependence of the resistance in a p-SiGe quantum well at various densities. 46 × 1011 cm−2 . 2 xx /(h/e ) = 1/(kF lD ). The numbers for this parameter were taken from the experimental data at the lowest available temperature. On the horizontal axis we plot the interaction parameter r¯s calculated from the corresponding carrier densities. A factor of 2 was taken into account for the Si-MOSFET system, which is the valley degeneracy gv on Si(100). Experiments on the metal–insulator transition have been typically performed as a function of gate voltage UG .
Power loss per carrier vs. hole temperature for two different hole densities. 1) where c1 and c2 are material specific constants and α = 5 (resp. 7) for deformation potential scattering with weak (resp. strong) screening and α = 3 (resp. 5) for piezoelectric coupling, again with weak (resp. strong) screening. The Tl -dependent terms in the above equation can be regarded as being constant in the experiment. In the double-logarithmic plot they are responsible for the strong increase of the dissipated power at the lowest electron temperatures.