Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

TL;DR

This paper calculates the polarization operator for planar charged fermions in a constant magnetic field within 2+1 dimensional QED at finite fermion density, with potential applications to graphene physics.

Contribution

It provides a novel calculation of the polarization tensor in QED$_{2+1}$ with nonzero fermion density and magnetic field, including the Green function at finite chemical potential.

Findings

Derived the Green function of Dirac fermions in magnetic field at finite chemical potential.

Calculated the polarization tensor considering real particles in energy levels.

Potential implications for observing effects in monolayer graphene under magnetic fields.

Abstract

The polarization operator (tensor) for planar charged fermions in constant uniform magnetic field is calculated in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) with a nonzero fermion density. We construct the Green function of the Dirac equation with a constant uniform external magnetic field in the QED$_{2+1}$ at the finite chemical potential, find the imaginary part of this Green function and then obtain the polarization tensor related to the combined contribution from real particles occupying the finite number of energy levels and magnetic field. We expect that some physical effects under consideration seem to be likely to be revealed in a monolayer graphene sample in the presence of external constant uniform magnetic field $B$ perpendicular to it.