Wide band gap semiconductor materials have drawn a lot of attention to the scientist owing to their diverse and promising future application in the power electronic devices, optical devices and photovoltaic industries such as Transistors, LED and Solar cells. The research on new wide band gap semiconductor materials, in particular GaN and GaN 2DEG heterostructure and the improvement of other existing semiconductor materials has been an important field of study in materials science, recently. To merge into a novel level of semiconductor physics and its future applications, it is inevitable to intensively study abnormal electron properties of these new materials especially in an extremely conditions such as in a very low temperature, high magnetic fields and in the Terahertz region.