On the thermodynamics of a degenerate two-dimensional electron gas in a strong magnetic field: density of states

Systematic expansions, in powers ofB^–1, for the free energy and the density of states, are derived for a two-dimensional degenerate electron gas in the presence of a strong magnetic field and an arbitrary potential. They are then applied to a system involving random impurities. Landau levels are shown to be broadened, with level widths related to the impurity concentration and potential. We show that level broadenings, induced by long range electron-impurity ineractions, do not depend on the magnetic field in the strong field limit, confirming the existing theories. But broadened Landau levels can have a large variety of shapes as one changes the impurity potential, distribution and concentration. Our theory, with a Gaussian potential, leads to a good agreement with the recent experiment on the de Haas-van Alphen effect in Br₂-graphite intercalation compounds