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

Abstract

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 (filling factor ${\nu }_0\lesssim 1$) with a quantum number $N_0\gg 1$ is considered. We uncover two regimes of renormalization by electron-electron interactions. In the first regime, where $N_0^{1/2}(1-{\nu }_0)\ll 1$, these interactions lead to a splitting of the Landau levels. In the second regime, where $N_0^{1/2}(1-{\nu }_0)\gg 1$, apart of the splitting, a renormalization of the bare Zeeman splitting occurs. The intermediate case $N_0^{1/2}(1-{\nu }_0)\approx 1$ cannot be studied within our approach. The applicability of the Fermi-liquid description is investigated for both regimes.

31 pages, 11 figures

References in corpus (1)

• Two - Dimensional Electron Liquid in a Weak Magnetic Field