Thermodynamical properties of a quasi two-dimensional electron gas under quantizing magnetic field

In this work, it is considered statistics of charge carries and found out basic thermodynamical magnitudes of quasi-two-dimensional systems under transverse quantizing magnetic field. On the basis of well-known thermodynamical relations, it is determined chemical potential, entropy and the equation of state, of the quasi-two-dimensional electron gas under quemtizing magnetic field. It is obtained general expressions for these magnitudes that are just at arbitrary value of the magnetic field and degree of degeneracy of the electron gas. In order obtain the analytical dependence of thermodynamical magnitudes upon temperature, magnetic field, concentration and parameters of energy spectrum, it is separately considered cases of the non-degenerated and strong degenerated electron gas. It is found out the criterion of degeneracy of the quasi-two-dimensional electron gas. It is shown that in the nondegenerate case, in contradistinction to the three-dimensional case, chemical potential, entropy and pressure depend on effective mass, which is perpendicular to the layers of the quasi-two-dimensional systems. There with the magnitude of chemical potential and entropy strongly increased in comparison with a three-dimensional case.It is performed compulations for the dependence of chemical potential and entropy upon temperature, magnetic field and the half-width of the one- dimensional conditions band. The analysis of these calculations shows, that chemical potential decreases and entropy increases with a rise to temperature. With increasing magnetic field, both chemical potential and entropy rises. It is shown that the decrease of the half-width of the one-dimensional conduction band promotes carrying out of electron gas degeneracy absence criterion. In the strong degenerate case, it is found out that entropy is determined in terms of the density of states, i.e. oscillates under quantizing magnetic field. This, in its turn, determines the behaviour, of thermopower under strong magnetic field, which in the case is expressed in terms of entropy