Cooper pairs are known to tunnel through a barrier between superconductors in a Josephson junction. The spin states of the pairs can be a mixture of singlet and triplet states when the barrier is an inhomogeneous magnetic material. The purpose of this thesis is to better understand the behavior of pair correlations in the ballistic regime for different magnetic configurations and varying physical parameters. We use a tight-binding Hamiltonian to describe the system and consider singlet-pair conventional superconductors. Using the Bogoliubov-Valatin transformation, we derive the Bogoliubov-de Gennes equations and numerically solve the associated eigenvalue problem. Pair correlations in the magnetic Josephson junction are obtained from the Green's function formalism for a superconductor. This formalism is applied to Josephson junctions composed of discrete and continuous magnetic materials. The differences between representing pair correlations in the time and frequency domain are discussed, as well as the advantages of describing the Gor'kov functions on a log scale rather than the commonly used linear scale, and in a rotating basis as opposed to a static basis. Furthermore, the effects of parameters such as ferromagnetic width, magnetization strength, and band filling will be investigated. Lastly, we compare results in the clean limit with known results in the diffusive regime.
|Commitee:||Ojeda-Aristizabal, Claudia, Peterson, Michael|
|School:||California State University, Long Beach|
|Department:||Physics and Astronomy|
|School Location:||United States -- California|
|Source:||MAI 58/02M(E), Masters Abstracts International|
|Subjects:||Computational physics, Physics, Condensed matter physics|
|Keywords:||Ballistic regime, Cooper pairs, Gor'kov functions, Josephson junction, Pair correlations, Rotating basis|
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