2020/01/31 by Gabriel C. Magalhães, Van S. Alves, Eduardo C. Marino +1 · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1103/physrevd.101.116005
published as Phys. Rev. D 101, 116005 (2020)
arxiv created 2020/05/13 · arxiv updated 2020/07/01
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 e2/(1+θ2), where θ 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 e2/(1+θ2) and e2θ/(1+θ2). Therefore, 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. 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 θ≈ 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.