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Lucas Sourrouille

Publications and source records attributed to Lucas Sourrouille.

At least 19 recordsLinked to original sources
arXiv2026

The gauge freedom in the Aharonov-Casher theorem: The problem in two and one dimensions

In this note, we investigate the role of gauge freedom in the Aharonov-Casher theorem in one and two dimensions. In particular, we analyze the asymptotic behavior of the gauge freedom. We show that in two dimensional space the gauge field is uniquely determined, whereas in one dimensional space there exists a gauge freedom that enables an infinite family of equivalent gauges. This freedom is determined by a constant k. However, the number $k$ must be restricted in order to guarantee the existence of a normalizable zero mode. This restriction is determined by the inequaly $|k| < \frac{1}{2} \int dx B(x)$, where $B(x)$ is a scalar field localized in a finite region of space. We show that this condition is equivalent to the gauge field taking opposite-sign values at $+\infty$ and $-\infty$. Finally, we illustrate these results with an explicit example.

quant-ph↗
arXiv2024

A note on degeneracy of excited energy levels in massless Dirac fermions

We propose a mechanism to construct the eigenvalues and eigenfunctions of the massless Dirac-Weyl equation in the presences of magnetic flux $Φ$ localized in a restricted region of the plane. Using this mechanism we analyze the degeneracy of the existed energy levels. We find that the zero and first energy level has the same $N+1$ degeneracy, where $N$ is the integer part of $\fracΦ{2π}$. In addition, and contrary to what is described in the literature regarding graphene, we show that higher energy levels are $N+m$ degenrate, beign $m$ the level of energy. In other words, this implies an indefinite growth of degenerate states as the energy level grows.

quant-ph↗
arXiv2023

Dynamic and static properties of Quantum Hall and Harmonic Oscillator systems on the non-commutative plane

We study two quantum mechanical systems on the noncommutative plane using a representation independent approach. First, in the context of the Landau problem, we obtain an explicit expression for the gauge transformation that connects the Landau and the symmetric gauge in noncommutative space. This lead us to conclude that the usual form of the symmetric gauge $\vec{A}=\left(-\fracβ{2}\hat{Y},\fracβ{2}\hat{X}\right)$, in which the constant $β$ is interpreted as the magnetic field, is not true in noncommutative space. We also be able to establish a precise definition of $β$ as function of the magnetic field, for which the equivalence between the symmetric and Landau gauges is hold in noncommutative plane. Using the symmetric gauge we obtain results for the spectrum of the Quantum Hall system, its transverse conductivity in the presence of an electric field and other static observables. These results amend the literature on Quantum Hall Effect in noncommutative plane in which the incorrect form of the symmetric gauge, in noncommutative space, is assumed. We also study the non-equilibrium dynamics of simple observables for this system. On the other hand, we study the dynamics of the harmonic oscillator in non-commutative space and show that, in general, it exhibit quasi-periodic behavior, in striking contrast with its commutative version. The study of the dynamics reveals itself as a most powerful tool to characterize and understand the effects of non-commutativity.

hep-th↗
arXiv2021

Landau levels for graphene layers in noncommutative plane

Starting from the zero modes of the single and bilayer graphene Hamiltonians we develop a mechanism to construct the eigenstates and eigenenergies for Landau levels in noncommutative plane. General formulas for the spectrum of energies are deduced, for both cases, single and bilayer graphene. In both cases we find that the effect to introduce noncommutative coordinates is a shift in the energy spectrum with respect to result obtained in commutative space.

hep-th↗
arXiv2019

Zero energy mode for an electron in graphene in a perpendicular magnetic field with constant asymptotics

We study the influence of a perpendicular magnetic field with the asymptotics $B(r\to \infty)= B_0$ in a electrons in graphene. It is shown that the zero-energy solutions can exist only for one pseudospin direction, depending on the sign of the magnetic field in the infinite boundary. This, shows that zero-energy level is robust with respect to possible inhomogeneities of the magnetic field. In addition, we show that the number of the states with zero energy for one pseudospin projection is infinity. These results should be useful in the study of ripples which cause a scattering of Dirac particles in slowly decreasing magnetic fields where the asymptotic states is easy to define.

quant-ph↗
arXiv2018

Magnetic superconfinement of Dirac fermions zero-energy modes in bilayer graphene quantum dots

We show that in bilayer graphene it is possible to achieve a very restrictive confinement of the massless Dirac fermions zero-modes by using inhomogeneous magnetic fields. Specifically, we show that, using a suitable nonuniform magnetic fields, the wave function may be restricted to a specific region of the space, being forbidden all transmission probability to the contiguous regions. This allows to construct mesoscopic structures in bilayer graphene by magnetic fields configurations.

cond-mat.mes-hall↗
arXiv2018

Spin-1/2 Landau levels in the symmetric gauge from the zero energy modes

Starting from the zero modes of the Dirac-Weyl equation for Landau levels in the symmetric gauge, we propose a novel mechanism to construct the eigenvalues and its eigenfunctions. We show that the problem may be addressed without numerical calculation and only solving the Dirac-Weyl equation for the zero modes. Specifically, the eigenstates associated to the negative magnetic field configurations may be constructed from the zero mode with positive chirality. In addition, we obtain that the eigenstates associated to the positive magnetic field configurations may be constructed from the zero mode with negative chirality. Finally, we show that our mechanism may be used to obtain the eigenvalues and eigenfunctions of the Hamiltonian corresponding to bilayer graphene system.

cond-mat.str-el↗
arXiv2017

Magnetization in pristine graphene with Zeeman splitting and variable spin-orbit coupling

The aim of this work is to describe the spin magnetization of graphene with Rashba spinorbit coupling and Zeeman effect. It is shown that the magnetization depends critically on the spin-orbit coupling l that is controlled with an external electric field. In turn, by manipulating the density of charge carriers, it is shown that spin up and down Landau levels mix introducing jumps in the spin magnetization. Two magnetic oscillations phases are described that can be tunable through the applied external fields. The maximum and minimum of the oscillations can be alternated by taking into account how the energy levels are filled when the Rashba-spin-orbit coupling is turned on. The results obtained are of importance to design superlattices with variable spin-orbit coupling with different configurations in which spin oscillations and spin filters can be developed.

cond-mat.str-el↗
arXiv2017

Ground state magnetization of conduction electrons in graphene with Zeeman effect

In this work we address the ground state magnetization in graphene, considering the Zeeman effect and taking into account the conduction electrons in the long wavelength approximation. We obtain analytical expressions for the magnetization at T=0 K, where the oscillations given by the de Haas van Alphen (dHvA) effect are present. We find that the Zeeman effect modifies the magnetization by introducing new peaks associated with the spin splitting of the Landau levels. These peaks are very small for typical carrier densities in graphene, but become more important for higher densities. The obtained results provide insight of the way in which the Zeeman effect modifies the magnetization, which can be useful to control and manipulate the spin degrees of freedom.

cond-mat.mtrl-sci↗
arXiv2017

Analytic solution for Gauged Dirac-Weyl equation in $(2+1)$-dimensions

A gauged Dirac-Weyl equation in (2+1)-dimension is considered. This equation has the particularity to describe the states of a graphene Dirac matter. In particular we are interested in matter interacting with a Chern-Simons gauge fields. We show that exact self-dual solutions are admitted. These solutions are the same as those supported by nonrelativistic matter interacting with a Chern-Simons gauge field.

hep-th↗
arXiv2016

Self-dual configurations in a generalized Abelian Chern-Simons-Higgs model with explicit breaking of the Lorentz covariance

We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions, $ω_1(|ϕ|)$ and $ω(|ϕ|)$, which split the kinetic term of the Higgs field - $|D_μϕ|^2 \rightarrowω_1 (|ϕ|)|D_0ϕ|^2-ω(|ϕ|) |D_kϕ|^2$ - breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whether $ω(|ϕ|) \propto β|ϕ|^{2β-2}$ with $β\geq 1$. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing function $ω_1(|ϕ|)$ which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual $|ϕ|^6$-vortex solutions have been analyzed both from theoretical and numerical point of view.

hep-th↗
arXiv2016

Note on generalization of Jackiw-Pi Vortices

We analyze two abelian Higgs systems with nonstandard kinetic terms. We consider a model involving the Maxwell term. For a particular choice of the nonstandard kinetics, we are able to obtain generalized Jackiw-Pi vortices. We, also, analyze a generalization of the Jackiw-Pi model. In that case we show that the system support the Nielsen-Olesen vortices as solutions.

hep-th↗
arXiv2015

Galilean symmetry in generalized abelian Schrödinger-Higgs models with and without gauge field interaction

We consider a generalization of nonrelativistic Schrödinger-Higgs Lagrangian by introducing a nonstandard kinetic term. We show that this model is Galilean invariant, we construct the conserved charges associated to the symmetries and realize the algebra of the Galilean group. In addition, we study the model in the presence of a gauge field. We also show that the gauged model is Galilean invariant. Finally, we explore relations between twin models and their solutions.

hep-th↗
arXiv2015

Maxwell-Higgs self-dual solitons on an infinite cylinder

We have studied the Maxwell-Higgs model on the surface of an infinite cylinder. In particular we show that this model supports self-dual topological soliton solutions on the infinite tube. Finally, the Bogomol'nyi-type equations are studied from theoretical and numerical point of view.

hep-th↗
arXiv2014

Self-dual soliton solutions in a Chern-Simons-CP(1) model with a nonstandard kinetic term

A generalization of the Chern-Simons-CP(1) model is considered by introducing a nonstandard kinetic term. For a particular case, of this nonstandard kinetic term, we show that the model support self-dual Bogomolnyi equations. The BPS energy has a bound proportional to the sum of the magnetic flux and the CP(1) topological charge. The self-dual equations are solved analytically and verified numerically.

hep-th↗
arXiv2014

A note on vortices from Lorentz-violating models

We consider two self-dual abelian Higgs systems obtained from Lorentz breaking symmetry models by dimensional reduction. For the first model, we show that the self-dual equations are identical to those of Nielsen-Olesen vortices. Also, we show that our vortices have electric charge. In the second case we show that self-dual Chern-Simons-Higgs vortices without electric charge are possible.

hep-th↗
arXiv2013

Self-dual Maxwell-Chern-Simons solitons from a Lorentz-violating model

Self-dual abelian Higgs system, involving both the Maxwell and Chern-Simons terms are obtained from Carroll-Field-Jackiw theory by dimensional reduction. Bogomol'nyi-type equations are studied from theoretical and numerical point of view. In particular we show that the solutions of these equations are Nielsen-Olesen vortices with electric charge.

hep-th↗