The fractional-dimensional space approach: Excitons and shallow impuritiesin semiconductor low-dimensional systems

The fractional-dimensional space approach is applied in the study of excito ns and shallow impurities in semiconductor low-dimensional systems. In this scheme, a real anisotropic semiconductor heterostructure in a three-dimens ional environment is treated as isotropic in an effective fractional-dimens ional space, and the value of the fractional dimension is associated to the degree of anisotropy of the actual three-dimensional semiconductor system. When a magnetic field is applied along the growth direction of the semicon ductor heterostructure, it introduces an additional degree of confinement a nd anisotropy besides the one imposed by the heterostructure barrier potent ial. The fractional dimension is then related to the anisotropy introduced both by the heterostructure barrier potential and magnetic field. In this w ork, we present results for excitons in GaAs-(Ga,Al)As quantum wells and sy mmetric-coupled double quantum wells, and shallow-impurity states in GaAs-( Ga,Al)As quantum wells and superlattices under growth-direction applied mag netic fields. Results are shown to be in good agreement with available expe rimental measurements and previous variational calculations.