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Superconductivity in multiple interface geometry: Applicability of quasiclassical theory
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
2001 (English)In: Journal of Low Temperature Physics, ISSN 0022-2291, E-ISSN 1573-7357, Vol. 124, no 1-2, 223-243 p.Article in journal (Refereed) Published
Abstract [en]

The method of two-point quasiclassical Green's function is reviewed and its applicability for description of multiple reflections/transmissions in layered structures is discussed. The Green's function of a sandwich built of super-conducting layers with a semi-transparent interface is found with the help of recently suggested quasiclassical method [A. Shelankov and M. Ozana, Phys. Rev. B 61. 7077 (2000)], as well as exactly, from thc Gor'kov equation. By the comparison of the results of the two approaches, thc validity of the quasiclassical method for thc description of real (non-integrable) systems is confirmed.

Place, publisher, year, edition, pages
2001. Vol. 124, no 1-2, 223-243 p.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-91463DOI: 10.1023/A:1017586120515ISI: 000170496900016OAI: oai:DiVA.org:umu-91463DiVA: diva2:736437
Conference
Symposium on Ultra Low Energy Physics - Methods and Phenomenology, JAN 10-14, 2001, POHJA, FINLAND
Available from: 2014-08-06 Created: 2014-08-05 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Mesoscopic superconductivity: quasiclassical approach
Open this publication in new window or tab >>Mesoscopic superconductivity: quasiclassical approach
2001 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This Thesis is concerned with the quasiclassical theory of meso-scopic superconductivity. The aim of the Thesis is to introduce the boundary conditions for a quasiclassical Green’s function on partially transparent interfaces in mesoscopic superconducting structures and to analyze the range of applicability of the quasiclassical theory. The linear boundary conditions for Andreev amplitudes, factoring the quasiclassical Green’s function, are presented.  The quasiclassical theory on classical trajectories is reviewed and then generalized to include knots with paths intersections.  The main focus of the Thesis is on the range of validity of the quasiclassical theory. This goal is achieved by comparison of quasiclassical and exact Green’s functions.  The exact Gor’kov Greens function cannot be directly used for the comparison because of its strong microscopic variations on the length-scale of λF. It is the coarse-grain averaged exact Green’s function which is appropriate for the comparison. In most of the typical cases the calculations show very good agreement between both theories. Only for certain special situations, where the classical trajectory contains loops, one encounters discrepancies. The numerical and analytical analysis of the role of the loop-like structures and their influence on discrepancies between both exact and quasiclassical approaches is one of the main results of the Thesis. It is shown that the terms missing in the quasiclassical theory can be attributed to the loops formed by the interfering paths.  In typical real samples any imperfection on the scale larger than the Fermi wavelength disconnects the loops and the path is transformed into the tree-like graph. It is concluded that the quasiclassical theory is fully applicable in most of real mesoscopic samples. In the situations where the conventional quasiclassical theory is inapplicable due to contribution of the interfering path, one can use the modification of the quasiclassical technique suggested in the Thesis.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2001. 56 p.
Keyword
mesoscopic superconductivity, quasiclassical theory, boundary conditions, multi-layer structures, Gor'kov equations, quasiclassical Green's function, Green's function on classical trajectories
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-91484 (URN)91-7305-161-6 (ISBN)
Public defence
2001-12-10, Naturvetarhuset, N320, Umeå universitet, Umeå, 10:30 (English)
Opponent
Supervisors
Available from: 2014-08-06 Created: 2014-08-06 Last updated: 2014-08-19Bibliographically approved

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