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

TL;DR

This paper investigates how electron-electron interactions affect Landau level splitting and Zeeman renormalization in a two-dimensional weakly interacting Fermi gas under a magnetic field, revealing two distinct regimes of behavior.

Contribution

It extends the diagram-technique formalism beyond Hartree-Fock to analyze interaction effects in a nearly filled Landau level, identifying two regimes of level renormalization.

Findings

Interaction causes Landau level splitting in one regime.

Zeeman splitting is renormalized in the other regime.

Fermi-liquid description's applicability varies between regimes.

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 $N^{1/2}_0(1-\nu_0) \ll 1$, these interactions lead to a splitting of the Landau levels. In the second regime, where $N^{1/2}_0(1-\nu_0) \gg 1$, apart of the splitting, a renormalization of the bare Zeeman splitting occurs. The intermediate case $N^{1/2}_0 (1-\nu_0)\approx 1$ cannot be studied within our approach. The applicability of the Fermi-liquid description is investigated for both regimes.