1-loop mass generation by a constant external magnetic field for an electron propagating in a thin medium

TL;DR

This paper calculates the one-loop self-energy of an electron in a thin medium under a magnetic field, revealing non-vanishing mass correction at zero mass and emphasizing the importance of considering all Landau levels.

Contribution

It provides a detailed quantum field theory calculation of electron self-energy in a graphene-like medium under magnetic field, highlighting the significance of all Landau levels in the mass correction.

Findings

Mass correction remains finite as m -> 0

All Landau levels must be considered for accurate results

Lowest Landau level approximation is insufficient

Abstract

The 1-loop self-energy of a Dirac electron of mass m propagating in a thin medium simulating graphene in an external magnetic field B is investigated in Quantum Field Theory. Equivalence is shown with the so-called reduced QED_{3+1} on a 2-brane. Schwinger-like methods are used to calculate the self-mass \delta m_{LLL} of the electron when it lies in the lowest Landau level. Unlike in standard QED_{3+1}, it does not vanish at the limit m -> 0 :\delta m_{LLL} -> (\alpha/2)\sqrt{pi/2}sqrt{\hbar|e|B/c^2}; all Landau levels of the virtual electron are taken into account and on mass-shell renormalization conditions are implemented. Restricting to the sole lowest Landau level of the virtual electron is explicitly shown to be inadequate. Resummations at higher orders lie beyond the scope of this work.