Electronic transport theory of the spin-dependent proximity effect in superconductor-ferromagnet heterostructures

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PhD Thesis by Dr. Peter Machon presents a comprehensive introduction to quasi-classical Green's function Theory for conventional superconductors and the Keldysh technique for non-equilibrium physics, featuring selected proofs and citations. It also introduces quantum circuit theory and a finite element approach for the Usadel equation. The work discusses extensions of circuit theory, four specific examples, and a general numerical solution algorithm. Key topics include: the extension of circuit theory to spin-dependent systems for superconductor-ferromagnet hybrid structures; the differential conductance of ferromagnetic insulator-superconductor heterostructures, revealing significant spin-mixing angles; the local and nonlocal thermoelectric effects in two- and three-terminal structures, alongside a generalization of the Onsager reciprocity relation; the giant thermoelectric effect in stacked and transistor-like structures of superconductors and ferromagnetic materials, achieving a large figure of merit (>1.75); local differential conductance and the search for equal spin triplet pairing in superconductor-ferromagnetic insulator-normal structures; and a generalized solution strategy for the discrete Usadel equation and BCS self-consistency relation, including a detailed description of numerical implementation and optimization techniques.