Induced Magnetic Field in a Finite Fermion Density Maxwell QED$_{2+1}$

TL;DR

This paper investigates the properties of magnetized states in Maxwell QED in 2+1 dimensions at finite fermion density, revealing that certain magnetized configurations can be energetically favorable compared to non-magnetized states.

Contribution

It demonstrates that magnetized states at finite fermion density can have lower energy, modeled by an effective Maxwell-Chern-Simons QED$_{2+1}$ Lagrangian with a gauge field mass.

Findings

Magnetized states can be energetically favored over non-magnetized states.

The effective theory includes a gauge field mass proportional to filled Landau levels.

Magnetized states are described by Maxwell-Chern-Simons QED$_{2+1}$.

Abstract

We are studying finite fermion density states in Maxwell QED$_{2+1}$ with external magnetic field. It is shown that at any fermion density the energy of some magnetized states may be less than that of the state with the same density, but no magnetic field. Magnetized states are described by the effective Maxwell-Chern-Simons QED$_{2+1}$ Lagrangian with gauge field mass proportional to the number of filled Landau levels.