Theory of Electron Transport in Superconducting Heterostructures
Sammanfattning: This thesis deals theoretically with electron transport in superconducting heterostructures. Depending on the system I use different theoretical approaches.The thesis contains an introduction followed by four research papers (Papers I-IV). The introduction gives the background of the work in Papers I-IV. Also, I discuss the theoretical methods used and some concepts of importance concerning transport processes. In Paper I, the difference between point-contact and sandwich-type tunneling in high-Tc junctions is studied. This difference is related to a periodically extended Anderson model with negative-U centers. The theoretical analysis is based on the tunneling Hamiltonian formalism and a slave boson representation to deal with the electron correlation problem. Qualitative agreement with experiment is found. In Papers II-III, supercurrent through superconductor-normal metal-superconductor (SNS) structures is studied, using the Bogoliubov-de Gennes equation. In Paper II, attention is paid to normal reflection due to a finite ratio between the gap .DELTA. and the Fermi energy .mY.. The dispersion relation of the Andreev levels is calculated. A minigap of the order .DELTA.2/.my. is found. The critical current is reduced due to the normal reflection. In Paper III, a double SNS junction is studied. The Andreev levels associated with different normal regions interact, leading to splitting of the levels. In the double SNS junction there is a contribution from the continuous levels to the current, in addition to the contribution from the discrete subgap levels. In Paper IV, the critical current density is calculated for a heterostructure, using Ginzburg-Landau theory. The variable parameter in the heterostructure is the mean free path, which is small in some region and large far away from the contaminated region. The product between the critical current and the resistance is explored, and found to increase with resistance. The connection between the model considered and grain boundaries in high-Tc superconductors is discussed.
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