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Mesoscopic superconductivity: quasiclassical approach
Umeå University, Faculty of Science and Technology, Department of Physics.
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 [en]
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: urn:nbn:se:umu:diva-91484ISBN: 91-7305-161-6 (print)OAI: oai:DiVA.org:umu-91484DiVA: diva2:736463
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
List of papers
1. Quasiclassical theory of superconductivity: A multiple-interface geometry
Open this publication in new window or tab >>Quasiclassical theory of superconductivity: A multiple-interface geometry
2000 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 61, no 10, 7077-7100 p.Article in journal (Refereed) Published
Abstract [en]

A method is suggested that allows one to study multiple coherent reflection/transmissions by partially transparent interfaces (e.g., in multilayer mesoscopic structures or grain boundaries in high T-c's), in the framework of the quasiclassical theory of superconductivity. It is argued that in the presence of interfaces, a straight-line trajectory transforms to a simple connected one-dimensional tree (graph) with knots, i.e., the points where the interface scattering events occur and pieces of the trajectories are coupled. For the two-component trajectory "wave function" which factorizes the Gor'kov matrix Green's function, a linear boundary condition on the knot is formulated for an arbitrary interface, specular or diffusive (in the many channel model). From the new boundary condition, we derive (i) the excitation scattering amplitude for the multichannel Andreev/ordinary reflection/transmission processes; (ii) the boundary conditions for the Riccati equation; (iii) the transfer matrix which couples the trajectory Green's function before and after the interface scattering. To show the usage of the method, the cases of a him separated from a hulk superconductor by a partially transparent interface, and a SIS' sandwich with finite thickness layers, are considered. The electric current response to the vector potential (the superfluid density rho(s)) with the pi phase difference in S and S' is calculated for the sandwich. It is shown that the model is very sensitive to imperfection of the SS' interface: the low temperature response being paramagnetic (rho(s) < 0) in the ideal system case, changes its sign and becomes diamagnetic (rho(s) > 0) when the probability of reflection is as low as a few percent.

National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-91464 (URN)10.1103/PhysRevB.61.7077 (DOI)000085985800086 ()
Available from: 2014-08-06 Created: 2014-08-05 Last updated: 2017-12-05Bibliographically approved
2. Superconductivity in multiple interface geometry: Applicability of quasiclassical theory
Open this publication in new window or tab >>Superconductivity in multiple interface geometry: Applicability of quasiclassical theory
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.

National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-91463 (URN)10.1023/A:1017586120515 (DOI)000170496900016 ()
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
3. Quasiclassical theory of superconductivity: Interfering paths
Open this publication in new window or tab >>Quasiclassical theory of superconductivity: Interfering paths
2002 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 65, no 1, 014510- p.Article in journal (Refereed) Published
Abstract [en]

We apply the method of a two-point quasiclassical Green's function to geometries where the trajectories include intefering paths and loops. For a system of two superconducting layers separated by a partially transparent interface, corrections to the quasiclassical solutions for the Green's function are explicitly found as well as the deviation from the normalization condition.

National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-91461 (URN)10.1103/PhysRevB.65.014510 (DOI)000173186000113 ()
Available from: 2014-08-06 Created: 2014-08-05 Last updated: 2017-12-05Bibliographically approved
4. Bogoliubov-de Gennes versus quasiclassical description of Josephson layered structures
Open this publication in new window or tab >>Bogoliubov-de Gennes versus quasiclassical description of Josephson layered structures
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.

National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-91460 (URN)10.1103/PhysRevB.66.054508 (DOI)000177873000114 ()
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
5. Squeezed states of a particle in magnetic field
Open this publication in new window or tab >>Squeezed states of a particle in magnetic field
1998 (English)In: Physics of the solid state, ISSN 1063-7834, E-ISSN 1090-6460, Vol. 40, no 8, 1276-1282 p.Article in journal (Refereed) Published
Abstract [en]

For a charged particle in a homogeneous magnetic field, we construct stationary squeezed states which are eigenfunctions of the Hamiltonian and the non-Hermitian operator (X) over cap(Phi) = (X) over cap cos Phi + (Y) over cap sin Phi, (X) over cap and (Y) over cap being the coordinates of the Larmor circle center and Phi is a complex parameter. In the family of the squeezed states, the quantum uncertainty in the Larmor circle position is minimal. The wave functions of the squeezed states in the coordinate representation are found and their properties are discussed. Besides, for arbitrary gauge of the vector potential we derive the symmetry operators of translations and rotations.

National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-91465 (URN)10.1134/1.1130543 (DOI)000075726400004 ()
Available from: 2014-08-06 Created: 2014-08-05 Last updated: 2017-12-05Bibliographically approved

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