Fenomenologia da Supercondutividade e Supercondutores Mesosc\'opicos Phenomenology of the superconductivity and mesoscopic superconductors

TL;DR

This paper presents a pedagogical development of the phenomenological Ginzburg-Landau theory of superconductivity, including applications to mesoscopic systems with surface defects, highlighting their impact on vortex dynamics.

Contribution

It offers a structured approach to teaching Ginzburg-Landau theory, incorporating time-dependent aspects and practical analysis of mesoscopic superconductors with defects.

Findings

Defects significantly affect vortex dynamics in mesoscopic superconductors.

The developed sequence enhances understanding of phase transitions and vortex behavior.

Application to systems with surface defects demonstrates their influence on superconducting properties.

Abstract

Em geral, quando a teoria fenomenol\'ogica de Ginzburg-Landau para supercondutores \'e trabalhada, pouco se esclarece aos alunos sobre a origem da mesma. Esta tem como base conceitos termodin\^amicos como fen\^omenos cr\'iticos e transi\c{c}\~oes de fase que, se devidamente tratados, enriquecem de sobremaneira a aula sobre tal assunto. Assim, neste trabalho apresentamos uma sequ\^encia para o desenvolvimento da principal teoria fenomenol\'ogica da supercondutividade. Iniciamos com uma breve introdu\c{c}\~ao aos fen\^omenos cr\'iticos e transi\c{c}\~oes de fase e, ent\~ao, desenvolvemos a teoria de Landau para transi\c{c}\~oes de fase de segunda ordem. Ap\'os isso, expomos a teoria de Ginzburg-Landau, e a teoria de Ginzburg-Landau dependente do tempo. Aplicamos esta \'ultima para o caso de dois sistemas supercondutores mesosc\'opicos, um homog\^eneo e outro com defeitos superficiais. Observa-se que os defeitos interferem de sobremaneira na din\^amica de v\'ortices do sistema. Palavras chave: Ginzburg-Landau, mesosc\'opico, v\'ortice, supercondutor In this work we present a sequence for the development of this major phenomenological theory for superconductors. We will begin with a brief introduction to the criticality and phase transitions phenomena e then we will describe the Landau theory for second order phase transitions. After that, we will introduce the Ginzburg-Landau theory and the time-dependent Ginzburg-Landau theory. As an application of this last one, we will study two mesoscopic systems. One of them a homogeneous sample and the other one a sample with surface defects. We show that the defects strongly influences the vortex dynamics of the system. Keywords: Ginzburg-Landau, mesoscopic, vortex, superconductor