We use pseudo-quantum electrodynamics in order to describe the full electromagnetic interaction of the p electrons in graphene in a consistent 2D formulation. We first consider the effect of this interaction in the vacuum polarization tensor or, equivalently, in the current correlator. This allows us to obtain the T → 0 conductivity after a smooth zero-frequency limit is taken in Kubo's formula. Thereby, we obtain the usual expression for the minimal conductivity plus corrections due to the interaction that bring it closer to the experimental value. We then predict the onset of an interaction-driven spontaneous quantum valley Hall effect below an activation temperature of the order of 2 K. The transverse (Hall) valley conductivity is evaluated exactly and shown to coincide with the one in the usual quantum Hall effect. Finally, by considering the effects of pseudo-quantum electrodynamics, we show that the electron self-energy is such that a set of P-and T-symmetric gapped electron energy eigenstates are dynamically generated, in association with the quantum valley Hall effect.

In this work, we study the chiral symmetry breaking in pseudo-quantum electrodynamics in (2 þ 1) dimensions, which is designed to reproduce a Coulomb potential for charged particles on a plane interacting via photons propagating in (3 þ 1) space-time dimensions and would be relevant for applications to condensed-matter systems. Using an ultraviolet cutoff in the momentum integrals, we show that there is a critical dimensionless coupling c ¼ =4 above which there is chiral symmetry breaking. In the case of the theory with N massless fermions, we obtain a critical value of the number of fermion flavors, N c , below which the chiral symmetry breaking occurs. Finally, we discuss the relevance of our results to graphene in the ultimate deep infrared regime where the Fermi velocity of the Dirac fermions approaches the velocity of light.

We examine the unitarity of a class of generalized Maxwell U(1) gauge theories in (2+1) D containing the pseudodifferential operator 1−α , for α ∈ [0, 1). We show that only Quantum Electrodynamics (QED3) and its generalization known as Pseudo Quantum Electrodynamics (PQED), for which α = 0 and α = 1/2, respectively, satisfy unitarity. The latter plays an important role in the description of the electromagnetic interactions of charged particles confined to a plane, such as in graphene or in hetero-junctions displaying the quantum Hall effect.