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Bogoliubov-de Gennes versus quasiclassical description of Josephson layered structures
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
2002 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 66, no 5, 054508- p.Article in journal (Refereed) Published
Abstract [en]

The applicability of the quasiclassical theory of superconductivity in Josephson multilayer structures is analyzed. The quasiclassical approach is compared with the exact theory based on the Bogoliubov-de Gennes equation. The angle- and energy-resolved (coarse-grain) currents are calculated using both techniques. It is shown that the two approaches agree in SIS'IS" geometries after the coarse-grain averaging. A quantitative discrepancy, which exceeds the quasiclassical accuracy, is observed when three or more interfaces are present. The invalidity of the quasiclassical theory is attributed to the presence of closed trajectories formed by sequential reflections from the interfaces.

Place, publisher, year, edition, pages
2002. Vol. 66, no 5, 054508- p.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-91460DOI: 10.1103/PhysRevB.66.054508ISI: 000177873000114OAI: oai:DiVA.org:umu-91460DiVA: diva2:736448
Note

Originally included in thesis in submitted form, with the title "Quasiclassical versus Bogolubov - de Gennes Theory of Multi-Layer Systems".

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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Shelankov, Andrei

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