A general formulation for the magnetic oscillations in two dimensional systems

We develop a general formalism for the magnetic oscillations (MO) in two dimensional (2D) systems. We consider general 2D Landau levels, which may depend on other variable or indices, besides the perpendicular magnetic field. In the ground state, we obtain expressions for the MO phase and amplitude. From this we use a Fourier expansion to write the MO, with the first term being a sawtooth oscillation. We also consider the effects of finite temperature, impurities or lattice imperfections, assuming a general broadening of the Landau levels. We develop two methods for describing these damping effects in the MO. One in terms of the occupancy of the Landau levels, the other in terms of reduction factors, which results in a generalization of the Lifshits-Kosevich (LK) formula. We show that the first approach is particularly useful at very low damping, when only the states close to the Fermi energy are excited. In contrast, the LK formula may be more convenient at higher damping, when only few terms are needed in its harmonic expansion. We compare different damping situations, showing how the MO are broadened in each case. The general formulation presented allows to relate the properties of the MO with those of the 2D systems. Graphical abstract