Microscopic-based screening theory of fractional quantized Hall effect

In this study, screening theory of the fractional quantized Hall effect that is observed in two dimensional charge systems induced in GaAs/AlGaAs heterostructures is investegated under the local approaches by analytical and numerical methods. By considering actual material properties for several samples and solving the three dimensional Poisson equation by numerical methods self-consistently, the electron density distributions are obtained. How these electron distributions change with the structure of the material are investigated, and also the effect of gating, chemical etching or trench gating methods are analyzed. Spatial positions and widths of the current-carrying channels (incompressible strips) that are formed at the selected magnetic fields are calculated, and the screening properties are examined. In addition to the fractional filling factor , the integer filling factors and the fractional filling factors are also studied. In a final step, interference properties of the filling factor are also investigated.