Study of a Two-Dimensional Electron Gas in a Magnetic Field.

The frequency- and density-dependent cyclotron effective mass and the frequency dependent relaxation time of the two-dimensional electron gas of a semiconducting surface inversion layer under a dc magnetic field are calculated. For this purpose, we have first studied the dielectric function. In the random phase approximation (RPA), hereafter called as the RPA, the real and imaginary parts of the dielectric function are evaluated for absolute zero and at finite temperature. We have considered three different cases: (a) No magnetic field (0(DEGREES)K and at finite temperature). The calculation is rather simple at 0(DEGREES)K and the result is reduced to the Stern's. But, in the finite temperature case, the calculation is already complicated because of the Fermi distribution function. (b) With a magnetic field at 0(DEGREES)K. The dielectric function has been expressed in terms of multiple summations, but this is now reduced to simpler form in terms of the Laguerre polynomials. (c) With a magnetic field at finite temperature. We have expanded the dielectric function in terms of dimensionless parameter (gamma), which is the ratio of the magnetic energy to twice the Fermi energy, this expansion is good especially for weak fields. In the presence of a field, the dielectric function shows cyclotron resonance whenever (omega) is integral multiple of (omega)(,c). We have eliminated this sharp resonance by introducing the broadening of the Landau levels due to collisions with impurities. By making use of these results, we have calculated the cyclotron effective mass and the relaxation time following the memory function technique. For the sake of simplicity, we have chosen a Gaussian impurity potential. The results for the apparent changes in mass with frequency and concentration are directly compared with two sets of experimental data. These theoretical results are found to be in good agreement with the experimental data of Wagner et al. 10% mass enhancement, when we adjust the parameters, n(,i)g('2) and d. The range dependence of the physical quantities, m* and 1/(tau), is found to be rather strong.