Multiple Landau level filling for a mean field limit of 2D fermions

TL;DR

This paper investigates the behavior of two-dimensional interacting fermions under strong magnetic fields, deriving a mean-field and semi-classical model for partially filled Landau levels relevant to quantum Hall phenomena.

Contribution

It introduces a new mean-field and semi-classical framework for understanding partially filled Landau levels in 2D fermion systems under strong magnetic fields.

Findings

Finite degeneracy of Landau levels established.

Fully filled Landau levels are inert with constant density.

Derived a limiting mean-field and semi-classical description for the last Landau level.

Abstract

Motivated by the quantum hall effect, we study N two dimensional interacting fermions in a large magnetic field limit. We work in a bounded domain, ensuring finite degeneracy of the Landau levels. In our regime, several levels are fully filled and inert: the density in these levels is constant. We derive a limiting mean-field and semi classical description of the physics in the last, partially filled Landau level.