Linearized Ginzburg-Landau Equation: Applications in the
Superconducting Nucleation Study.

Name: Gabriel Ayres Marçal
Type: MSc dissertation
Publication date: 29/12/2021

Namesort descending Role
Jorge Luis Gonzalez Alfonso Co-advisor *
Valberto Pedruzzi Nascimento Advisor *

Examining board:

Namesort descending Role
Jorge Luis Gonzalez Alfonso Co advisor *
Magda Bittencourt Fontes External Examiner *
Valberto Pedruzzi Nascimento Advisor *
Wanderlã Luis Scopel Internal Examiner *

Summary: Superconductivity is a topic of condensed matter physics that has been extensively studied due to its potential for technological applications. Superconducting materials have good applicability due to their property of conducting electrical current without energy losses (without electrical
resistance) besides having a perfect diamagnetism when cooled down the critical temperature. These materials are being widely used in various technologies for public transport vehicles, electrical energy storage, medical and hospital equipment, motors for electrical energy transformation, superconducting equipment and currently in the manufacture of superconducting switches (Josephson junctions).
In this dissertation, we addressed aspects and properties of superconductivity, such as the Meissner Effect (magnetic field expulsion), zero resistivity, critical fields and temperatures, types
of superconductors, among others.We also discussed theories that have emerged during the years to explain the superconducting phenomena (London, BCS and Ginzburg-Landau). We turned our attention to the Ginzburg-Landau theory which was developed by expanding the free energy of the system by powers of the order parameter, around the critical temperature (temperature above which the superconductivity of a particular system is vanished), in order to explain the thermodynamic properties of the transition from the normal state to the superconducting state. In this theory, the order parameter characterizes the superconducting state and it assumes non-zero values below the critical temperature.
Specifically, we performed a theoretical study of the Ginzburg-Landau linearized equation and its application to the study of superconductivity nucleation in thin-film systems with or without Ginzburg-Landau edge conditions or with steplike magnetic domain structures. For each case,
a MATLAB algorithm using the finite difference method was used to solve numerically the respective linearized equation, providing the dependence of the critical temperature on the magnetic field and the location of the order parameter of samples with dimensions of the order of the coherence length. The analogy between the linearized Ginzburg-Landau equation for a global sample in the presence of a magnetic field with the Schrödinger equation for a quantum double harmonic oscillator revealed the wave character of superconducting nucleation.

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