Proximity effect of the superconductivity in metallic superlattices and a self-similar multilamellar system

Yuan, B. J. (1989) Proximity effect of the superconductivity in metallic superlattices and a self-similar multilamellar system. Masters thesis, Memorial University of Newfoundland.

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Abstract

In the thesis, the various theories of inhomogeneous superconductivity based on Gor'kov's equations(Chapter 2) are reviewed including de Gennes-Werthamer theory and Eilenberger equations as well as their applications to study the proximity effect of a bilayer system. McMillan's tunnelling model is also introduced. The characteristics of the thickness dependence of the transition temperature Tc in the thin film limit from the above theories are discussed and will be compared with the results from our calculation. -- The superconductivity of a superlattice consisting of alternating superconducting and normal layers has been investigated(Chapter 3) by means of the Bogoliubov equation. A relation, which determines the transition temperature Tc, is obtained from the self-consistency equation of the order parameter. The analytical expression of the dependence of the transition temperature Tc on the thickness of a superconducting layer in the thin film limit has been obtained through an analysis of the equation and the comparison with the results from the other theories discussed in Chapter 2 has been done. A periodic energy-momentum relation reflecting the periodicity of the structure has been obtained which gives rise to the basis for any further calculation for the presence of an external magnetic field or a finite order parameter. -- In Chapter 4, we applied the Werthamer theory to a quasi-periodic geometry with a fractional dimension D. We build the recurrence relation of the coefficients in the linear fractional transformation in terms of the self-similarity of the geometry, which provides a systematic method to deal with the complicated boundary conditions. The dependence of the transition temperature on both the thickness of the superconducting layer and fractional dimension D has been obtained by the scaling argument in some limiting cases. The scaling argument is also extended to the case of the presence of a perpendicular magnetic field. The numerical calculation for transition temperature as a function of the thickness is completed and shown in the corresponding figures. We also calculate certain values of Tc corresponding to the given parameters, such as dimension D, thickness ds and coherence length ξ||(0), used in the experiment and compare the theoretical results from the calculation with the experimental values. The result of the comparison is satisfactory and the discrepancies ranging from 2% → 10%, consistent with the Werthamer theory.

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