arXiv subjects

Gabriel C. Magalhães

Publications and source records attributed to Gabriel C. Magalhães.

5 recordsLinked to original sources

arXiv2021

Effects of the Pseudo-Chern-Simons action for strongly correlated electrons in the plane

Chiral symmetry breaking comes from the mass dynamically generated through interaction of Dirac fermions for both quantum electrodynamics in (2+1)D (QED3) and (3+1)D (QED4). In QED3, the presence of a Chern-Simons (CS) parameter affects the critical structure of the theory, favoring the symmetric phase where the electron remains massless. Here, we calculate the main effects of a Pseudo-Chern-Simons (PCS) parameter $θ$ into the dynamical mass generation of Pseudo quantum electrodynamics (PQED). The $θ$-parameter provides a mass scale for PQED at classical level and appears as the pole of the gauge-field propagator. After calculating the full electron propagator with the Schwinger-Dyson equation at quenched-rainbow and large-$N$ approximations, we conclude that $θ$ affects the critical parameters related to the fine-structure constant, $α_c(θ)$, and to the number of copies of the matter field, $N_c(θ)$, by favoring the symmetric phase. In the continuum limit ($Λ\to \infty$), nevertheless, the $θ$-parameter do not affect the critical parameters. We also compare our analytical results with numerical findings of the integral equation for the mass function of the electron.

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arXiv2021

Bosonization, mass generation, and the pseudo Chern-Simons action

We discuss several aspects of a generalization of the Chern-Simons action containing the pseudo-differential operator$\sqrt{-\Box}$, which we shall call pseudo Chern-Simons (PCS). Firstly, we derive the PCS from the bosonization of free massive Dirac particles in (2+1)D in the limit when $m^2\ll p^2$, where $m$ is the fermion mass and $p$ is its momentum. In this regime, the whole bosonized action also has a modified Maxwell term, involving the same pseudo-differential operator. Furthermore, the large-mass $m^2\gg p^2$ regime is also considered. We also investigate the main effects of the PCS term into the Pseudo quantum electrodynamics (PQED), which describes the electromagnetic interactions between charged particles in (2+1)D. We show that the massless gauge field of PQED becomes massive in the presence of a PCS term, without the need of a Higgs mechanism. In the nonrelativistic limit, we show that the static potential has a repulsive term (given by the Coulomb potential) and an attractive part (given by a sum of special functions), whose competition generates bound states of particles with the same charge. Having in mind two-dimensional materials, we also conclude that the presence of a PCS term does not affect the renormalization either of the Fermi velocity and of the band gap in a Dirac-like material.

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arXiv2020

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

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 $e^2/(1+θ^2)$, 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 $e^2/(1+θ^2)$ and $e^2θ/(1+θ^2)$. 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 $θ\approx 0.36$. This behavior is an important signature of the model and relations with doping control of band gap size are also discussed in the conclusions.

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arXiv2017

Two-dimensional Yukawa interaction driven by a nonlocal-Proca quantum electrodynamics

We derive two versions of an effective model to describe dynamical effects of the Yukawa interaction among Dirac electrons in the plane. Such short-range interaction is obtained by introducing a mass term for the intermediate particle, which may be either scalar or an abelian gauge field, both of them in (3+1) dimensions. Thereafter, we consider that the matter field propagates only in (2+1) dimensions, whereas the bosonic field is free to propagate out of the plane. Within these assumptions, we apply a mechanism for dimensional reduction, which yields an effective model in (2+1) dimensions. In particular, for the gauge-field case, we use the Stueckelberg mechanism in order to preserve gauge invariance. We refer to this version as nonlocal-Proca quantum electrodynamics (NPQED). For both scalar and gauge cases, the effective models reproduce the usual $e^{-m r}/r$ Yukawa interaction in the static limit. By means of perturbation theory at one loop, we calculate the mass renormalization of the Dirac field. Our model is a generalization of Pseudoquantum electrodynamics (PQED), which is a gauge-field model that provides a Coulomb interaction for two-dimensional electrons. Possibilities of application to Fermi-Bose mixtures in mixed dimensions, using cold atoms, are briefly discussed.

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arXiv2015

Suppressing vacuum fluctuations with vortex excitations

The Casimir force for a planar gauge model is studied considering perfect conducting and perfect magnetically permeable boundaries. By using an effective model describing planar vortex excitations, we determine the effect these can have on the Casimir force between parallel lines. Two different mappings between models are considered for the system under study, where generic boundary conditions can be more easily applied and the Casimir force be derived in a more straightforward way. It is shown that vortex excitations can be an efficient suppressor of vacuum fluctuations. In particular, for the model studied here, a planar Chern-Simons type of model that allows for the presence of vortex matter, the Casimir force is found to be independent of the choice of boundary conditions, at least for the more common types, like Neumann, perfect conducting and magnetically permeable boundary conditions. We give an interpretation for these results and some possible applications for them are also discussed.

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