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

Abstract

We revisit the Coleman-Hill theorem in the context of reduced planar QED. Using the global U(1) Ward identity for this nonlocal 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-noninvariant 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.