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We study a microscopic model for a disordered superlattice system, which simulates the effect of intrinsic alloy fluctuation on localization in alloy superlattices. Numerical investigation of scaling behavior of the localization length shows that excitations along and perpendicular to the superlattice axis undergo a localization transition at a nonzero critical disorder. Therefore, we contend that for localization, the alloy superlattices should be viewed as a 3-dimensional anisotropic material. At the transition, the localization length diverges with critical exponent v = 1.2 ± 0.2. We expect that the model belongs to the same universality class as the 3 dimensional isotropic Anderson model.

Spatial and dynamical properties of optical phonons in AlxGa1−xAs alloys and GaAs/AlxGa1−xAs quantum wells are studied. An isotopically disordered harmonic crystal model is developed to study spatial properties of optical phonons in AlxGa1−xAs alloys. In the GaAs/AlxGa1−xAs system, transmission of the GaAs optical phonons through an AlxGa1−xAs barrier is studied using three-dimensional lattice dynamical model, fully accounting for the random arrangement of Ga and Al atoms in the alloy barrier. In the AlxGa1−xAs alloy, a localized-to-extended transition is found as a function of x. In GaAs/AlxGa1−xAs quantum wells, the transmission coefficient of the GaAs LO phonons through the alloy barrier remains significant below x < 0.3. These results are in good qualitative agreement with the experimentally deduced coherence length of LO phonons from nonequilibrium hot phonon populations.

Bifractal is a highly anisotropic structure where planar fractals are stacked to form a 3-dimensional lattice. The localization lengths along fractal structure for the Anderson model defined on a bifractal are calculated. The critical disorder and the critical exponent of the localization lengths are obtained from the finite size scaling behavior. The numerical results are in a good agreement with previous results which have been obtained from the localization lengths along the perpendicular direction. This suggests that the anisotropy of the embedding lattice structure is irrelevant to the critical properties of the localization., 3 pages, source TeX file and 3 epsi figures. submitted to PRB

We discuss a few examples of cases in which the widely used mean-field approaches to alloys and alloy superlattices may not give complete solutions. These examples include the anomalously large Stokes and anti-Stokes real space-charge transfer over thick alloy barriers and the spatial extent of optical phonons in alloys and alloy superlattices, which have remained unsolved or controversial. We argue, both theoretically and experimentally, that approaches that fully account for inhomogeneities, partial ordering, and disorder effects in the alloys as well as the proper understanding of coupled quantum-mechanical systems do give answers to these important puzzles.