Nonuniform vortex distributions in superconductors: from critical state to conformal crystals

Detalhes bibliográficos
Autor(a) principal: MENEZES, Raí Maciel de
Data de Publicação: 2017
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Institucional da UFPE
Texto Completo: https://repositorio.ufpe.br/handle/123456789/25302
Resumo: In this dissertation, we study through numerical simulation, properties of the vortex matter in superconductors. In non-homogeneous superconductors, the penetration of magnetic flux (provided by the vortex entry) within the sample is theoretically described by the macroscopic critical state models, where due to interaction with material impurities (pinning centres), the vortex density is high near the edges and decreases as we approach the center of the sample. Although extensively studied, the critical state models do not explain in detail how the microscopic events lead to the global behavior predicted by the macroscopic models , especially nearby the surfaces, where the vortex currents are deformed to satisfy the boundary conditions. We simulate through molecular dynamics methods the penetration and the microscopic dynamics of vortices in a superconducting slab subjected to a parallel applied magnetic field. We explicitly take into account the often neglected vortex-surface interaction and analyse how this can influence the dynamics and the critical state configurations. We then verify which of the various critical state models best describes the system. Nearby the surfaces, we observed regions with zero density of vortices, which arise due to the energetic barrier that hinders the vortex entry and exit. Such regions, known as flux free regions, have a thickness which depends on the strength of the applied magnetic field and the level of pinning forces in the material. We also analyse the temporal evolution of the flux front inside the superconductor and the hysteresis cycles of the magnetization due to an external field variation, and compare with results known in the literature. Another topic of broad interest concerns the possible ordered structures that the vortex lattice can form. In situations of uniform density the system of vortices converges to a minimum of energy and tends to be ordered as a triangular lattice (Abrikosov lattice). However, in situations where the vortices may form nonuniform distributions, due to variations in sample thickness, interactions with material inhomogeneities, among other ways, the triangular Abrikosov lattice will not satisfy the minimum energy condition. The question is whether the nonuniform distribution of vortices presents a structure of small domains of different densities, i.e., a nonuniform glass, or a new ordered structure emerges. We obtain evidences of conformal crystals as possible, stable nonuniform vortex configurations in a superconductor. Such configuration is an example of ordered crystallization in a nonuniform particle distribution. These ordered structures, although can present local inhomogeneities, preserve the topological order and can be mathematically mapped into a triangular lattice through a conformal transformation. We propose a simple method to obtain the particle density required to observe such structures and suggest possible experimental realizations in which conformal (or quasiconformal) vortex crystals could be observed in bulk superconductors or thin films.
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spelling MENEZES, Raí Maciel dehttp://lattes.cnpq.br/3507338537387806http://lattes.cnpq.br/8076432608646837SILVA, Clécio Clemente de Souza2018-07-31T22:09:57Z2018-07-31T22:09:57Z2017-03-06https://repositorio.ufpe.br/handle/123456789/25302In this dissertation, we study through numerical simulation, properties of the vortex matter in superconductors. In non-homogeneous superconductors, the penetration of magnetic flux (provided by the vortex entry) within the sample is theoretically described by the macroscopic critical state models, where due to interaction with material impurities (pinning centres), the vortex density is high near the edges and decreases as we approach the center of the sample. Although extensively studied, the critical state models do not explain in detail how the microscopic events lead to the global behavior predicted by the macroscopic models , especially nearby the surfaces, where the vortex currents are deformed to satisfy the boundary conditions. We simulate through molecular dynamics methods the penetration and the microscopic dynamics of vortices in a superconducting slab subjected to a parallel applied magnetic field. We explicitly take into account the often neglected vortex-surface interaction and analyse how this can influence the dynamics and the critical state configurations. We then verify which of the various critical state models best describes the system. Nearby the surfaces, we observed regions with zero density of vortices, which arise due to the energetic barrier that hinders the vortex entry and exit. Such regions, known as flux free regions, have a thickness which depends on the strength of the applied magnetic field and the level of pinning forces in the material. We also analyse the temporal evolution of the flux front inside the superconductor and the hysteresis cycles of the magnetization due to an external field variation, and compare with results known in the literature. Another topic of broad interest concerns the possible ordered structures that the vortex lattice can form. In situations of uniform density the system of vortices converges to a minimum of energy and tends to be ordered as a triangular lattice (Abrikosov lattice). However, in situations where the vortices may form nonuniform distributions, due to variations in sample thickness, interactions with material inhomogeneities, among other ways, the triangular Abrikosov lattice will not satisfy the minimum energy condition. The question is whether the nonuniform distribution of vortices presents a structure of small domains of different densities, i.e., a nonuniform glass, or a new ordered structure emerges. We obtain evidences of conformal crystals as possible, stable nonuniform vortex configurations in a superconductor. Such configuration is an example of ordered crystallization in a nonuniform particle distribution. These ordered structures, although can present local inhomogeneities, preserve the topological order and can be mathematically mapped into a triangular lattice through a conformal transformation. We propose a simple method to obtain the particle density required to observe such structures and suggest possible experimental realizations in which conformal (or quasiconformal) vortex crystals could be observed in bulk superconductors or thin films.CNPqNesta dissertação, estudamos através de simulação computacional, propriedades da matéria de vórtices em supercondutores. Em supercondutores não homogêneos, a penetração do fluxo magnético (proporcionada pela entrada de vórtices) no interior da amostra é descrita teoricamente pelos modelos macroscópicos de estado crítico, onde devido à interação com as impurezas do material, a densidade de vórtices é alta próximo às bordas e decresce à medida que nos aproximamos do centro da amostra. Apesar de terem sido bastante estudados, os modelos de estado crítico não respondem detalhadamente qual a conexão dos eventos microscópicos com os resultados dos modelos macroscópicos, principalmente nas imediações da superfície, onde as correntes dos vórtices são deformadas para satisfazer as condições de contorno. Simulamos através de métodos de dinâmica molecular a penetração e a dinâmica microscópica de vórtices em um filme supercondutor devido à presença de um campo magnético aplicado paralelamente à sua superfície. Reproduzimos a interação dos vórtices com a superfície do supercondutor e analisamos como isso pode influenciar na dinâmica e nas configurações de estado crítico. Verificamos então qual dentre os vários modelos de estado crítico descreve melhor o sistema. Nas imediações da superfície, observamos regiões com densidade nula de vórtices, as quais surgem devido a barreira energética que retarda a entrada e a saída das linhas de fluxo no supercondutor. Tais regiões, conhecidas como flux free regions, têm uma espessura que depende da intensidade do campo magnético aplicado e do nível de impurezas do material. Analisamos também a evolução temporal da frente de fluxo dentro do supercondutor e os ciclos de histerese da magnetização devidos à variação de um campo magnético externo e comparamos com resultados conhecidos na literatura. Outro olhar interessante é em relação as possíveis estruturas ordenadas que a rede de vórtices pode formar. Em situações de densidade uniforme, o sistema converge para um mínimo de energia e tende a se ordenar como uma rede triangular (rede de Abrikosov). Entretanto, em situações em que os vórtices podem formar distribuições não uniformes, devido variações na espessura da amostra, interações com inomogeneidades do material, dentre outras maneiras, a rede triangular de Abrikosov não satisfará a condição de mínima energia. A questão é se a distribuição não uniforme de vórtices apresenta uma estrutura de pequenos domínios de diferentes densidades, i.e., um vidro não uniforme, ou se uma nova estrutura ordenada emerge. Obtemos evidências da formação de cristais conformes como uma rede estável de vórtices em um supercondutor. Tal formação é um exemplo de cristalização ordenada da rede em uma distribuição de partículas não uniforme. Estas estruturas ordenadas, embora possam apresentar inomogeneidades locais, preservam a ordem topológica e podem ser matematicamente mapeadas em uma rede triangular através de uma transformação conforme. Propomos um método simples para gerar a densidade de partículas necessária para a observação de tais estruturas e sugerimos possíveis experimentos nos quais cristais conformes de vórtices, ou quase conformes, poderiam ser observados em supercondutores volumosos e filmes finos.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em FisicaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessSupercondutividadeVórticesCristais conformesNonuniform vortex distributions in superconductors: from critical state to conformal crystalsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILDISSERTAÇÃO Raí Maciel de Menezes.pdf.jpgDISSERTAÇÃO Raí Maciel de Menezes.pdf.jpgGenerated Thumbnailimage/jpeg1258https://repositorio.ufpe.br/bitstream/123456789/25302/5/DISSERTA%c3%87%c3%83O%20Ra%c3%ad%20Maciel%20de%20Menezes.pdf.jpgf2f4ce9f25652287c64c24af6e61cc8fMD55ORIGINALDISSERTAÇÃO Raí Maciel de Menezes.pdfDISSERTAÇÃO Raí Maciel de Menezes.pdfapplication/pdf14678819https://repositorio.ufpe.br/bitstream/123456789/25302/1/DISSERTA%c3%87%c3%83O%20Ra%c3%ad%20Maciel%20de%20Menezes.pdf2b9fa367b413e137b34bea260db2a99bMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv Nonuniform vortex distributions in superconductors: from critical state to conformal crystals
title Nonuniform vortex distributions in superconductors: from critical state to conformal crystals
spellingShingle Nonuniform vortex distributions in superconductors: from critical state to conformal crystals
MENEZES, Raí Maciel de
Supercondutividade
Vórtices
Cristais conformes
title_short Nonuniform vortex distributions in superconductors: from critical state to conformal crystals
title_full Nonuniform vortex distributions in superconductors: from critical state to conformal crystals
title_fullStr Nonuniform vortex distributions in superconductors: from critical state to conformal crystals
title_full_unstemmed Nonuniform vortex distributions in superconductors: from critical state to conformal crystals
title_sort Nonuniform vortex distributions in superconductors: from critical state to conformal crystals
author MENEZES, Raí Maciel de
author_facet MENEZES, Raí Maciel de
author_role author
dc.contributor.authorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/3507338537387806
dc.contributor.advisorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/8076432608646837
dc.contributor.author.fl_str_mv MENEZES, Raí Maciel de
dc.contributor.advisor1.fl_str_mv SILVA, Clécio Clemente de Souza
contributor_str_mv SILVA, Clécio Clemente de Souza
dc.subject.por.fl_str_mv Supercondutividade
Vórtices
Cristais conformes
topic Supercondutividade
Vórtices
Cristais conformes
description In this dissertation, we study through numerical simulation, properties of the vortex matter in superconductors. In non-homogeneous superconductors, the penetration of magnetic flux (provided by the vortex entry) within the sample is theoretically described by the macroscopic critical state models, where due to interaction with material impurities (pinning centres), the vortex density is high near the edges and decreases as we approach the center of the sample. Although extensively studied, the critical state models do not explain in detail how the microscopic events lead to the global behavior predicted by the macroscopic models , especially nearby the surfaces, where the vortex currents are deformed to satisfy the boundary conditions. We simulate through molecular dynamics methods the penetration and the microscopic dynamics of vortices in a superconducting slab subjected to a parallel applied magnetic field. We explicitly take into account the often neglected vortex-surface interaction and analyse how this can influence the dynamics and the critical state configurations. We then verify which of the various critical state models best describes the system. Nearby the surfaces, we observed regions with zero density of vortices, which arise due to the energetic barrier that hinders the vortex entry and exit. Such regions, known as flux free regions, have a thickness which depends on the strength of the applied magnetic field and the level of pinning forces in the material. We also analyse the temporal evolution of the flux front inside the superconductor and the hysteresis cycles of the magnetization due to an external field variation, and compare with results known in the literature. Another topic of broad interest concerns the possible ordered structures that the vortex lattice can form. In situations of uniform density the system of vortices converges to a minimum of energy and tends to be ordered as a triangular lattice (Abrikosov lattice). However, in situations where the vortices may form nonuniform distributions, due to variations in sample thickness, interactions with material inhomogeneities, among other ways, the triangular Abrikosov lattice will not satisfy the minimum energy condition. The question is whether the nonuniform distribution of vortices presents a structure of small domains of different densities, i.e., a nonuniform glass, or a new ordered structure emerges. We obtain evidences of conformal crystals as possible, stable nonuniform vortex configurations in a superconductor. Such configuration is an example of ordered crystallization in a nonuniform particle distribution. These ordered structures, although can present local inhomogeneities, preserve the topological order and can be mathematically mapped into a triangular lattice through a conformal transformation. We propose a simple method to obtain the particle density required to observe such structures and suggest possible experimental realizations in which conformal (or quasiconformal) vortex crystals could be observed in bulk superconductors or thin films.
publishDate 2017
dc.date.issued.fl_str_mv 2017-03-06
dc.date.accessioned.fl_str_mv 2018-07-31T22:09:57Z
dc.date.available.fl_str_mv 2018-07-31T22:09:57Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.language.iso.fl_str_mv eng
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dc.publisher.none.fl_str_mv Universidade Federal de Pernambuco
dc.publisher.program.fl_str_mv Programa de Pos Graduacao em Fisica
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publisher.none.fl_str_mv Universidade Federal de Pernambuco
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