Fundamentals of Superconducting Nanoelectronics

326 Pages·2011·8.51 MB·English

by  A. A. Varlamov (auth.), Anatolie Sidorenko (eds.)

NanoScience and Technology
NanoScience and Technology
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Anatolie Sidorenko
Editor
Fundamentals
of Superconducting
Nanoelectronics
With 496 Figures
123
Editor
Prof.Dr. Anatolie Sidorenko
Academy of Science of Moldova
Institute of Electronic Engineering and Nanotechnologies
Academiei Street 3/3, 2028 Chisinau, Moldova
E-mail:
Foreword
Over the last decade, we have witnessed a large number of novel developments and
rapid progress in superconducting electronics. This has been triggered by mainly
two facts:
• The use of novel physical phenomena, which have been theoretically predicted
already during the previous decades but detected only recently in superconduct-
ing materials.
• The astonishing advances in thin film and nanotechnology, which allows us
the reproducible fabrication of the superconducting devices and circuits with
nanometer resolution.
This pleasant development is also reflected in a considerable increase in funding
and investments related to the field of superconducting electronics. An increase by
almost a factor of three has been observed worldwide over the last decade.
The main goal of this book is to give a profound insight into the basic
phenomena occurring in superconductors and hybrid systems composed of super-
conductors and other materials such as ferromagnets on a nanometer scale (e.g.,
Fulde–Ferrell–Larkin–Ovchinikov state, triplet superconductivity, crossed Andreev
reflection, coherent dynamics of superconducting junctions). Moreover, this book
provides a comprehensive overview on the application of these phenomena in novel
nanoelectronic devices and circuits (e.g., SIS tunnel junction phase detectors, pi-
junction-based logic circuits, superconducting spintronic devices). Information on
these new developments so far has to be collected from publications in technical
journals or presentations at conferences and workshops. Therefore, the collection of
review papers presented in this book provides a valuable overview on the Frontiers
of Superconducting Electronics, ranging from the discussion of the theoretical
background and the experimental study of the phenomena to their application in
novel devices. Although it is impossible to cover all aspects of broad and complex
field of superconducting electronics, this book addresses the most interesting
phenomena and key developments of the last decade in a comprehensive way.
v
vi Foreword
The book is organized as following: Chapter 1 is devoted to one of the
fundamental problems of superconductivity – fluctuations, which are also important
for numerous technical applications of superconductivity such as ultra-sensitive
detectors. Chapter 2 deals with the experimental study of superconducting fluctua-
tions in systems with reduced dimensionality – nanowires. Chapters 3 and 4 present
the results of both theoretical (Chap. 3) and experimental (Chap. 4) studies of the
crossed Andreev reflection and nonlocal transport phenomena in superconductor–
ferromagnet hybrid structures. Since there has been a particularly rapid progress
in the new research area of superconducting spintronics, this book puts special
emphasis on the advanced theoretical description (Chaps. 5–7) as well as the
experimental study of superconductor–ferromagnet hybrid structures (Chap. 8).
Chapter 9 shows how point-contact spectroscopy of superconducting materials can
be used as a powerful method for the investigation of the energy gap and the
electron–phonon interaction in superconductors. In Chaps. 10 and 11, supercon-
ducting integrated receivers and cryogenic phase-lock loop systems are presented
as prominent examples on how theoretical concepts, novel physics, and advanced
fabrication technologies can be combined to achieve smart superconducting devices.
The authors of the chapters and the editor of the book Prof. Anatolie Sidorenko
are well-known leading specialists, who have been involved in various research
programs dealing with superconducting devices and their applications. All of them
were former lecturers at NATO-ARW and NATO-ASI.
This book will be useful for a broad readership including researchers, engineers,
lecturers, Ph.D. students, and all others, who would like to gain insight into the
Frontiers of Superconductivity at nanoscale.
Garching Rudolf Gross
June 2011
Preface
The idea to write this book appeared after a series of workshops devoted to
superconductivity of low-dimensional objects, which we organized last decade. In
2004 director of Walther-Meißner-Institut Professor Rudolf Gross and I organized
an NATO Advanced Research Workshop “Nanoscale Devices, Fundamentals and
Applications” and published the book with the same title, collecting the best of
reports, presented on that workshop. As we realized a bit later, the book was
in demand by colleagues, who deal with applications of superconductivity. For
example, the group of researchers is engaged in development and fabrication of a
very sensitive superconducting sensor for infrared radiation, superconducting thin-
film bolometer, would like to achieve the highest possible sensitivity. They develop
different technological processes for improvement of the quality of the supercon-
ducting film, trying to obtain thin films with the narrowest width of superconducting
transition. In case, when a member of such group has knowledge in superconducting
fluctuations (which are rather noticeable for low-dimensional objects) that there
exists a limitation of the smallest possible width of the superconducting transition,
Tc, given by the Ginsburg criteria, Tc D GiTc, then such group of researchers
can save a lot of time and instead of many experimental attempts to improve the
quality of the films, just select the most suitable material with the smallest value
of the parameter Gi. This is a simple example how the knowledge of the intrinsic
phenomena in superconductivity at nanoscale can help the experimentalists to save
their resources and time to achieve the desirable result.
Recently, some very interesting effects were first predicted theoretically and then
detected experimentally in layered and low-dimensional superconductors – triplet
superconductivity, crossed Andreev reflection, and pi-shift. How one can use them
for novel devices? What kind of nanostructures should be prepared for detection
and application of those effects? In order to highlight some of the rosen questions,
well-known experts were invited to write chapters for this book.
vii
viii Preface
We believe that the book can attract attention of researchers, engineers, Ph.D.
students and others, who would like to gain knowledge about some intrinsic effects
of Superconductivity at nanoscale.
Kishinev, June 2011 Anatolie Sidorenko
Contents
1 “Fluctuoscopy” of Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
A.A. Varlamov
1.1 Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Thermodynamic Superconductive Fluctuations Close
to Tc0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Rather Rayleigh–Jeans Fields than
Boltzmann Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Manifestation of SF Close to Tc . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Ginzburg–Landau Theory.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 GL Functional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Zero Dimensionality: The Exact Solution
for the Heat Capacity Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.3 Zero Dimensionality: The Exact Solution
for the Fluctuation Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.4 Fluctuation Diamagnetism in Lead Nanoparticles . . . . . . . . 15
1.4 Fluctuation Thermodynamics of Layered
Superconductor in Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.1 Lawrence–Doniach Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.2 General Formula for the Fluctuation Free
Energy in Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.4.3 Fluctuation Magnetization of Layered
Superconductor and its Crossovers . . . . . . . . . . . . . . . . . . . . . . . . 20
1.5 Fluctuation Conductivity of Layered Superconductor .. . . . . . . . . . . . . 23
1.5.1 Time-Dependent GL Equation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5.2 General Expression for Paraconductivity .. . . . . . . . . . . . . . . . . 25
1.5.3 Paraconductivity of a Layered Superconductor . . . . . . . . . . . 27
1.5.4 In-Plane Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.5.5 Out-of Plane Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5.6 Analysis of the Limiting Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5.7 Comparison with the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.6 Quantum Superconductive Fluctuations Above Hc2.0/ . . . . . . . . . . . . 33
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