Localization in three-dimensional systems by a Gaussian random potential

The electronic localization properties of a three-dimensional (3D) cubic system under the influence of a random potential having a Gaussian probability distribution are studied by the potential-well-analogy method. The results are compared with the localization-function method as well as with numerical results using the strip method. The overall shape and size of the mobility-edge trajectory is found to be significantly different than the one obtained using a rectangular distribution for the random potential. In contrast to the case of the rectangular distribution for the random potential, where the mobility edge at the band center was located at W=16.5 V, the corresponding effective $W_c$ for the Gaussian distribution is found at $W_c$=21.5 V. We have confirmed this prediction by performing numerical calculations using one-parameter scaling in 3D strips.