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Orientador: Luiz Antonio Barreiro / Banca: Alexandre Mesquita / Banca: Denis Eduardo Peixoto / Resumo: O objetivo desse trabalho concentra-se em estudar uma nova metodologia para resolução de problemas em matéria condensada, nos quais as partículas estão fortemente acopladas, não permitindo um tratamento perturbativo padrão. Esse método, originário da dualidade AdS/CFT (Anti-de Sitter/Conformal Field Theory), está sendo conhecido na comunidade de matéria condensada como Dualidade Holográfica. Como aplicação desta teoria, o comportamento de supercondutores foi escolhido. A metodologia da dualidade holográfica utiliza uma teoria de campos em um espaço-tempo curvo. Partindo da ação associada é possível obter as equações de movimento das partículas envolvidas. A seguir foi empregado o uso do software Mathematica-Wolfram, para a resolução das Equações Diferenciais através do Método de Frobenius. Os resultados obtidos expressam que os valores esperados de operadores, as chamadas funções de correlação, são bem similares à curva de intervalo de energia previsto pela teoria BCS em função da temperatura. Também infere-se a partir da fórmula de Kubo, que os resultados numéricos da condutividade elétrica, claramente indicam uma condutividade infinita abaixo de uma determinada temperatura crítica Tc, resultando em um supercondutor / Abstract: The objective of this work is to study a new methodology for solving problems in condensed matter, in which the particles are strongly coupled, not allowing a standard perturbative treatment. This method, originating from the AdS / CFT (Anti-Sitter / Conformal Field Theory) duality, is being known in the condensed matter community as Holographic Duality. As an application of this theory, the behavior of superconductors was chosen. The holographic duality methodology uses a field theory in a curved space-time. From the associated action it is possible to obtain the equations of motion of the particles involved. Next, the use of the Mathematica-Wolfram software was used to solve the Differential Equations by the Frobenius Method. The obtained results express that the expected values of operators, so-called correlation functions, are very similar to the energy interval curve predicted by the BCS theory as a function of temperature. It is also inferred from the Kubo formula that the numerical results of electrical conductivity clearly indicate an infinite conductivity below a given critical temperature Tc, resulting in a superconductor / Mestre

Local Hall probe measurements and differential magneto-optical imaging with high spatial resolution have been used to investigate the magnetic state of high temperature superconducting Bi2Sr2CaCu2O8+� (BSCCO) micro-disks and platelet single crystals. The results obtained by magneto-optical imaging demonstrate that the field at which flux quantised vortices enter the disks decays exponentially with increasing temperature and the measured data agree well with analytic models for the thermal excitation of individual pancake vortices over Bean-Livingston surface barriers. Scanning Hall probe microscopy images are used to directly map the magnetic induction profiles of individual micro-disks at different applied fields and the results can be quite successfully fitted to analytic models which assume a continuous distribution of flux in the sample. At low fields, however, the characteristic mesoscopic compression of vortex clusters in increasing magnetic fields has been observed. Even at higher fields, where single vortex resolution is lost, it is still possible to track configurational changes in the vortex patterns, since competing vortex orders impose unmistakable signatures on local magnetisation curves as a function of the applied field. These observations are in excellent agreement with molecular dynamics numerical simulations which lead to a natural definition of the lengthscale for the crossover between discrete and continuum behaviours in this system. In closely related experiments, Hall magnetometry is used to probe the out-of-plane local magnetisation of platelet BSCCO single crystals. The magnetisation is found to depend on the strength and direction of an in-plane magnetic field in the crossing vortex lattices regime. The remanent magnetisation in zero out-of-plane field is found to exhibit a pronounced anisotropy, being largest with the in-plane field parallel to the crystalline a-axis, and smallest when it is parallel to the orthogonal b-axis. This behaviour is attributed to the presence of underlying linear disorder. Finally, spectral analysis of the local magnetisation data is used to estimate a lower cutoff for the characteristic frequency of thermal fluctuations of vortex positions.

Lau Wai Chuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 93-94). / Lau Wai Chuen. / Contents --- p.ii / List of Figures --- p.iv / List of Tables --- p.vi / Abstract --- p.ix / Acknowledgement --- p.x / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Superconductivity --- p.1 / Chapter 1.2 --- The Hubbard model and the Extended Hubbard model --- p.3 / Chapter 1.3 --- Gap Equation --- p.6 / Chapter 1.3.1 --- One-dimensional solutions --- p.11 / Chapter 1.3.2 --- Two-dimensional solutions --- p.12 / Chapter Chapter 2. --- Solving BCS equation --- p.15 / Chapter 2.1 --- Zero value of the denominator of the BCS equations --- p.15 / Chapter 2.2 --- Discontinuity of the BCS equations --- p.16 / Chapter Chapter 3. --- Results of BCS equations for finite size clusters --- p.34 / Chapter 3.1 --- Method used to solve BCS equations --- p.34 / Chapter 3.2 --- Results for the one dimensional and two dimensional lattices --- p.34 / Chapter 3.2.1 --- Extended S-wave solution --- p.35 / Chapter 3.2.2 --- P-wave and D-wave solutions --- p.36 / Chapter Chapter 4. --- Results of BCS equations compare with exact solutions --- p.69 / Chapter 4.1 --- "An exact solution of D-wave, Ne=2" --- p.69 / Chapter 4.2 --- Comparison of the ground state energy with the results calculated by exact diagonalization --- p.73 / Chapter Chapter 5. --- The Phase Diagram of the superconducting state --- p.78 / Chapter Chapter 6. --- Conclusion --- p.91 / Bibliography --- p.93

Quantum phenomena in high-Tc superconductors and dimerized quantum Heisenberg antiferromagnets are studied analytically in this thesis. The implications of the Fermi surface consisting of the disjoint pieces, observed in cuprate superconductors, are considered. It is demonstrated that in this case the g-wave superconducting pairing is closely related to d-wave pairing. The superconductivity in this system can be described in terms of two almost degenerate superconducting condensates. As a result a new spatial scale lg, much larger than the superconducting correlation length x, arises and a new collective excitation corresponding to the relative phase oscillation between condensates, the phason, should exist. The Josephson tunneling for such a two-component system has very special properties. It is shown that the presence of g-wave pairing does not contradict the existing SQUID experimental data on tunneling in the ab-plane. Possible ways to experimentally reveal the g-wave component and the phason in a single tunnel junction, as well as in SQUID experiments, are discussed. The dimerized quantum spin models studied in this thesis include double-layer and alternating chain Heisenberg antiferromagnets. To account for strong correlations between the S=1 elementary excitations (triplets) in the dimerized phase; the analytic Brueckner diagram approach based on a description of the excitations as triplets above a strong-coupling singlet ground state; has been applied. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Analytical calculations of physical observables are in excellent agreement with numerical data.Results obtained for double layer antiferromagnet near the (zero temperature) quantum critical point coincide with those previously obtained within the nonlinear s model approach Additional singlet (S=0) and triplet (S=1) modes are found as two-particle bound states of the elementary triplets in the Heisenberg chain with frustration.

Graduation date: 1996

Thesis (Ph. D.)--University of Chicago, August 1999. / Includes bibliographical references. Also available on the Internet.