Comments on the Chern-Simons photon term in the QED description of graphene

TL;DR

This paper confirms that the topological photon self-energy in reduced planar QED, relevant for graphene, remains unchanged beyond one-loop order, supporting the stability of topological effects in non-Lorentz-invariant conditions.

Contribution

It extends the Coleman-Hill theorem to non-local, gauge-invariant reduced planar QED with Lorentz non-invariance, relevant for graphene.

Findings

Topological photon self-energy does not receive higher-order quantum corrections.

The Ward identity confirms the stability of the topological term.

Relevance to time parity odd dynamics in graphene.

Abstract

We revisit the Coleman-Hill theorem in the context of reduced planar QED. Using the global U(1) Ward identity for this non-local but still gauge invariant theory, we can confirm that the topological piece of the photon self-energy at zero momentum does not receive further quantum corrections apart from the potential one-loop contribution, even when considering the Lorentz non-invariant case due to the Fermi velocity $v_F<c$. This is of relevance to probe possible time parity odd dynamics in a planar sheet of graphene which has an effective description in terms of $(2+1)$-dimensional planar reduced QED.