arXiv subjects

W. B. De Lima

Publications and source records attributed to W. B. De Lima.

5 recordsLinked to original sources

arXiv2023

Vortices in a parity-invariant Maxwell-Chern-Simons model

In this work we propose a parity-invariant Maxwell-Chern-Simons $U(1) \times U(1)$ model coupled with two charged scalar fields in $2+1$ dimensions, and show that it admits finite-energy topological vortices. We describe the main features of the model and find explicit numerical solutions for the equations of motion, considering different sets of parameters and analyzing some interesting particular regimes. We remark that the structure of the theory follows naturally from the requirement of parity invariance, a symmetry that is rarely envisaged in the context of Chern-Simons theories. Another distinctive aspect is that the vortices found here are characterized by two integer numbers.

hep-th↗

arXiv2022

Self-dual Maxwell-Chern-Simons solitons in a parity-invariant scenario

We present a self-dual parity-invariant $U(1) \times U(1)$ Maxwell-Chern-Simons scalar $\text{QED}_3$. We show that the energy functional admits a Bogomol'nyi-type lower bound, whose saturation gives rise to first order self-duality equations. We perform a detailed analysis of this system, discussing its main features and exhibiting explicit numerical solutions corresponding to finite-energy topological vortices and non-topological solitons. The mixed Chern-Simons term plays an important role here, ensuring the main properties of the model and suggesting possible applications in condensed matter.

hep-th↗

arXiv2021

On the ultraviolet finiteness of parity-preserving $U(1) \times U(1)$ massive QED$_3$

The parity-preserving $U_A(1)\times U_a(1)$ massive QED$_3$ is ultraviolet finiteness -- exhibits vanishing $β$-functions, associated to the gauge coupling constants (electric and pseudochiral charges) and the Chern-Simons mass parameter, and all the anomalous dimensions of the fields -- as well as is parity and gauge anomaly free at all orders in perturbation theory. The proof is independent of any regularization scheme and it is based on the quantum action principle in combination with general theorems of perturbative quantum field theory by adopting the Becchi-Rouet-Stora (BRS) algebraic renormalization method in the framework of Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) subtraction scheme.

hep-th↗

arXiv2021

On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

We analyze the Schrödinger operator in two-dimensions with an attractive potential given by a Bessel-Macdonald function. This operator is derived in the non-relativistic approximation of planar quantum electrodynamics (${\rm QED}_3$) models as a framework for evaluation of two-quasiparticle scattering potentials. The analysis is motivated keeping in mind the fact that parity-preserving ${\rm QED}_3$ models can provide a possible explanation for the behavior of superconductors. Initially, we study the self-adjointness and spectral properties of the Schrödinger operator modeling the non-relativistic approximation of these ${\rm QED}_3$ models. Then, by using {\em Setô-type estimates}, an estimate is derived of the number of two-particle bound states which depends directly on the value of the effective coupling constant, $C$, for {\em any} value of the angular momentum. In fact, this result in connection with the condition that guarantees the self-adjointness of the Schrödinger operator shows that there can always be a large number of two-quasiparticle bound states in planar quantum electrodynamics models. In particular, we show the existence of an isolated two-quasiparticle bound state if the effective coupling constant $C \in (0,2)$ in case of zero angular momentum. To the best of our knowledge, this result has not yet been addressed in the literature. Additionally, we obtain an explicit estimate for the energy gap of two-quasiparticle bound states which might be applied to high-$T_c$ $s$-wave Cooper-type superconductors as well as to $s$-wave electron-polaron--electron-polaron bound states (bipolarons) in mass-gap graphene systems.

math-ph↗

arXiv2020

On the electron-polaron--electron-polaron scattering and Landau levels in pristine graphene-like quantum electrodynamics

The parity-preserving $U(1)\times U(1)$ massless QED$_3$ is proposed as a pristine graphene-like planar quantum electrodynamics model. The spectrum content, the degrees of freedom, spin, masses and charges of the quasiparticles (electron-polaron, hole-polaron, photon and Néel quasiparticles) which emerge from the model are discussed. The four-fold broken degeneracy of the Landau levels, similar as the one experimentally observed in pristine graphene submitted to high applied external magnetic fields, is obtained. Furthermore, the model exhibits zero-energy Landau level indicating a kind of anomalous quantum Hall effect. The electron-polaron--electron-polaron scattering potentials in $s$- and $p$-wave states mediated by photon and Néel quasiparticles are computed and analyzed. Finally, the model foresees that two electron-polarons ($s$-wave state) belonging to inequivalent $\mathbf{K}$ and $\mathbf{K^\prime}$ points in the Brillouin zone might exhibit attractive interaction, while two electron-polarons ($p$-wave state) lying both either in $\mathbf{K}$ or in $\mathbf{K^\prime}$ points experience repulsive interaction.

hep-th↗