Estimation of the cyclotron mass from the de Haas–van Alphen oscillation in the two-dimensional and quasi-two-dimensional multiband systems

It is known that a cyclotron mass is obtained by fitting a temperature dependence of the Fourier harmonics of the de Haas--van Alphen oscillation to the temperature reduction factor in the Lifshitz-Kosevich (LK) formula in which the oscillation of the chemical potential is neglected. The LK formula, however, should be applied carefully in two-dimensional (2D) and quasi-two-dimensional (Q2D) systems at low temperatures, where the magnetic-field dependence of the chemical potential cannot be neglected. We compare the effective cyclotron mass, which is estimated by using the temperature reduction factor for the fixed chemical potential, with the cyclotron mass of the system. The cyclotron mass is fairly well obtained in 2D single-band systems when the density of states of the reservoir is negligible or much larger than the density of states of the 2D band. On the other hand, if the reservoir has the same order of the density of states as the 2D band, the effective cyclotron mass is shown to be estimated about 7% larger at low temperature and high field. In the 2D multiband systems the effective cyclotron mass for the heavier mass is underestimated about 9%, while the lighter effective cyclotron mass is obtained with very small errors.