Oscillations of chemical potential, magnetizations and head capacity under magnetic field of two dimensional electron gas

In this study, a Two-dimesional electron gas which is formed in $\delta$-doped GaAlAs/GaAs/GaAlAs and in a AlGaN/GaN/AlGaN quantum well are considered. First, for both systems the results of self-consistent calculations are used. A magnetic field is applied on 2DEG in the growth direction which is perpendicular to the plane in which the electrons move freely. The direction of the field in our study is the $z$-direction and the plane on which the electrons move freely is the $xy$ plane. When the effect of the magnetic field is considered, first of all, the density of states (DOS) of the systems is considered. In the absence of magnetic field, 2DEG has a constant DOS but in the presence of magnetic field DOS shows delta like singularities (at Landau levels) and these singularities change because of defects in the system. Scattering and defects of the system result in the expansion of these levels. In the present study the level broadening is assumed to be Gaussian like and DOS is calculated numerically. It is seen that the variation of DOS as a function of magnetic field is effective for all properties of 2DEG. First the behaviour of Fermi energy is examined and calculated for different electron concentrations as a function of applied magnetic field. In the next step, magnetization of the system is obtained as a change in internal energy with respect to magnetic field $B$. And also heat capacity of 2DEG is studied as a temperature rate of change of internal energy. It is shown that these thermodynamic properties of the system make oscillations together with the Fermi energy. We observed many oscillations for low field values, in high field region we observe only few oscillations but they became very clear.