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

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.

References in corpus (25)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Topological Insulators
• Black phosphorus field-effect transistors
• Chiral tunneling and the Klein paradox in graphene
• Epitaxial Growth of a Silicene Sheet
• Dirac cones reshaped by interaction effects in suspended graphene
• Direct Determination of Band Gap Renormalization in Photo-Excited Monolayer MoS2
• Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory
• Dynamical Chiral Symmetry Breaking on a Brane in Reduced QED
• Aspects of Chern-Simons Theory
• Interaction Induced Quantum Valley Hall Effect in Graphene
• Unitarity of theories containing fractional powers of the d'Alembertian operator
• Spontaneous Chiral-Symmetry Breaking in Three-Dimensional QED with a Chern--Simons Term
• On Higher Spatial Derivative Field Theories
• Renormalization group aspects of graphene
• Spin g-factor due to electronic interactions in graphene
• Chiral-Symmetry Breaking in Pseudo Quantum Electrodynamics at Finite Temperature
• Quantum-electrodynamical approach to the exciton spectrum in Transition-Metal Dichalcogenides
• Comments on the Chern-Simons photon term in the QED description of graphene
• Dynamical Mass Generation in Pseudo Quantum Electrodynamics with Four-Fermion Interactions
• Two-dimensional Yukawa interaction driven by a nonlocal-Proca quantum electrodynamics
• The effect of a Chern-Simons term on dynamical gap generation in graphene
• Parity anomaly cancellation in a three-dimensional QED with single massless Dirac fermion
• Abelian Chern-Simons Theory for the Fractional Quantum Hall Effect in Graphene

Cited by in corpus (11)

• Electron-Photon Vertex and Dynamical Chiral Symmetry Breaking in Reduced QED: An Advanced Study of Gauge Invariance
• Effects of the Pseudo-Chern-Simons action for strongly correlated electrons in the plane
• Non-perturbative field theoretical aspects of graphene and related systems
• On the supersymmetric pseudo-QED
• Bosonization, mass generation, and the pseudo Chern-Simons action
• Classical features, Anderson-Higgs mechanism, and unitarity in Lee-Wick pseudo-electrodynamics
• Non-relativistic solutions for three-body molecules within a Chern-Simons model
• The Lee-Wick-Chern-Simons pseudo-quantum electrodynamics
• Effective potential of scalar Lee-Wick pseudo-electrodynamics
• The influence of a conducting surface on the conductivity of graphene
• Remarks on classical pseudo-electrodynamics