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We study a nonlocal theory that combines both the Pseudo quantumelectrodynamics (PQED) and Chern-Simons actions among two-dimensionalelectrons. In the static limit, we conclude that the competition of these twointeractions yields a Coulomb potential with a screened electric charge givenby $e^2/(1+\theta^2)$, where $\theta$ is the dimensionless Chern-Simonsparameter. This could be useful for describing the substrate interaction withtwo-dimensional materials and the doping dependence of the dielectric constantin graphene. In the dynamical limit, we calculate the effective current-currentaction of the model considering Dirac electrons. We show that this resemblesthe electromagnetic and statistical interactions, but with two differentoverall constants, given by $e^2/(1+\theta^2)$ and $e^2\theta/(1+\theta^2)$.Therefore, the $\theta$-parameter does not provide a topological mass for theGauge field in PQED, which is a relevant difference in comparison with quantumelectrodynamics. Thereafter, we apply the one-loop perturbation theory in ourmodel. Within this approach, we calculate the electron self-energy, theelectron renormalized mass, the corrected gauge-field propagator, and therenormalized Fermi velocity for both high- and low-speed limits, using therenormalization group. In particular, we obtain a maximum value of therenormalized mass for $\theta\approx 0.36$. This behavior is an importantsignature of the model and relations with doping control of band gap size arealso discussed in the conclusions.

Pseudo Quantum Electrodynamics and Chern-Simons theory Coupled to Two-dimensional Electrons