Magnetization and Orbital Properties of the Two-Dimensional Electron Gas in the Quantum Limit

In a two-dimensional electron gas, incompressible states at specific filling factors induce discontinuous jumps ΔM in the magnetization. The amplitudes of the jumps are related to the energy gap Δµ between compressible states. When probing ΔM, it is possible to learn how physical parameters, such as disorder, spin-polarization and Coulomb interactions affect Δμ, the incompressibility gap. In these lectures, the relation between the particular orbital structures found at integer and fractional filling factors, the thermodynamic density of states, the corresponding current distributions and the orbital magnetization are emphasized. The non-equilibrium states very often encountered at incompressible filling-factors due to the absence of dissipation are also discussed.