Abstract
We study a nonlocal theory that combines both the Pseudo quantum electrodynamics (PQED) and Chern-Simons actions among two-dimensional electrons. In the static limit, we conclude that the competition of these two interactions yields a Coulomb potential with a screened electric charge given by $e^2/(1+\theta^2)$, where $\theta$ is the dimensionless Chern-Simons parameter. This could be useful for describing the substrate interaction with two-dimensional materials and the doping dependence of the dielectric constant in graphene. In the dynamical limit, we calculate the effective current-current action of the model considering Dirac electrons. We show that this resembles the electromagnetic and statistical interactions, but with two different overall 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 the Gauge field in PQED, which is a relevant difference in comparison with quantum electrodynamics. Thereafter, we apply the one-loop perturbation theory in our model. Within this approach, we calculate the electron self-energy, the electron renormalized mass, the corrected gauge-field propagator, and the renormalized Fermi velocity for both high- and low-speed limits, using the renormalization group. In particular, we obtain a maximum value of the renormalized mass for $\theta\approx 0.36$. This behavior is an important signature of the model and relations with doping control of band gap size are also discussed in the conclusions.
Highlights
Quantum electrodynamics (QED) is one of the most well-succeed theories in physics, in particular, because of the remarkable comparison between the experimental data for the electron g-factor and its theoretical prediction
We study a nonlocal theory that combines both the pseudo quantum electrodynamics (PQED) and Chern-Simons actions among two-dimensional electrons
The θ-parameter does not provide a topological mass for the gauge field in PQED, which is a relevant difference in comparison with quantum electrodynamics
Summary
Quantum electrodynamics (QED) is one of the most well-succeed theories in physics, in particular, because of the remarkable comparison between the experimental data for the electron g-factor and its theoretical prediction. Aiming for applications in condensed matter physics, several results have been obtained from this approach, for example, dynamical mass generation [8], interaction driven quantum valley Hall effect [9], quantum corrections of the electron g-factor [10], Yukawa potential in the plane [11], and electron-hole pairing (excitons) in transition metal dichalcogenides [12]. All of these applications neglect the interaction of the matter with the ChernSimons action at tree level. In Appendix B, we calculate the renormalized mass and in Appendix C we calculate the beta functions through the renormalization group for our model
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