Mal'nev Vadim (Professor)Sewnet Belayneh2018-06-192023-11-092018-06-192023-11-092014-06http://10.90.10.223:4000/handle/123456789/1776In this thesis, we represent Classical Hall Effect and Quantum Hall Effect studies at high magnetic field and low temperature in 2DEG and in high quality and charge carrier bilayer graphene samples for the degenerate Landau levels, with a particular emphasis on Integer and Fractional Quantum Hall effects. And also we have studied about the equation of quantization energy (Landau levels) by using Landau gauge and symmetric gauge solutions in 2DEG and bilayer graphene samples. In 2DEG and in bilayer graphene, the thermal energy is less than quantization energy (<=T ≪ ℏ @A) and degeneracy (g) is greater than or equal to total number of electrons. In this situation Quantum Hall Effect can be observed with quantized Hall resistances and plateaus for integer and fractional filing factorenLandau levels and hall effectThesis