Magnetization in two-dimensional electron gas in a perpendicular magnetic field: the roles of edge states and spin-orbit coupling

We study the de Haas--van Alphen (dHvA) oscillations in the magnetization of a two-dimensional electron gas (2DEG) under the influence of the edge states and/or the Rashba spin-orbit interaction (SOI). The boundaries of the systems lift partially the degeneracies of Landau levels (LL's) and the resulting edge states lead to the changes of both the center and the amplitude of the sawtoothlike magnetization oscillation. The SOI mixes the spin-up and spin-down states of neighboring LL's into two unequally spaced energy branches. The inclusion of SOI changes the well-defined sawtooth pattern of the dHvA oscillations in the magnetization. The weaker the magnetic field is, the larger is the change of the dHvA oscillations due to the edge effect and/or the spin-orbit coupling. Some theoretical results are compared with the experimental data.