Two-dimensional weakly interacting Fermi gas in a magnetic field: Level splitting

We apply the diagram-technique formalism beyond the Hartree-Fock approximation to a two-dimensional nearly ideal electron gas in a weak perpendicular magnetic field. The case of an almost completely filled upper Landau level [for its filling factor ν₀ holds (1-ν₀)<<1] with a quantum number N₀>>1 is considered. We uncover two regimes of renormalization by electron-electron interactions. In the first regime, where N^1/2₀(1-ν₀)<<1, these interactions lead to a splitting of the Landau levels. In the second regime, where N^1/2₀(1-ν₀)>>1, apart of the splitting, a renormalization of the bare Zeeman splitting occurs. The intermediate case N^1/2₀(1-ν₀)~1 cannot be studied within our approach. The applicability of the Fermi-liquid description is investigated for both regimes.