Modern Aspects of Superconductivity: Theory of Superconductivity

306 Pages·2021·25.6 MB·English

by  Sergei Kruchinin

Modern Aspects
of
Superconductivity
Theory of Superconductivity
Second Edition
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Modern Aspects
of
Superconductivity
Theory of Superconductivity
Second Edition
Sergei Kruchinin
Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine
World Scientific
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MODERN ASPECTS OF SUPERCONDUCTIVITY
Theory of Superconductivity
Second Edition
Copyright © 2021 by World Scientific Publishing Co. Pte. Ltd.
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ISBN 978-981-123-451-4 (hardcover)
ISBN 978-981-123-452-1 (ebook for institutions)
ISBN 978-981-123-453-8 (ebook for individuals)
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“The single reason for our inability to treat the problems of
superconductivity consists in the absence of a sufficient
imagination.”
Richard P. Feynman
v
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Preface
The study in the field of superconductivity theory is one of the most bright,
fruitful,andpromisingtrendsinthetheoretical physicsofcondensedmatter,
since superconductivity remains to be one of the most interesting research
areas in physics.
The goal of the book is to give representation of certain modern
aspects of superconductivity. We discuss such important aspects of the
theory of superconductivity as the nature of high-Tc superconductivity, two-
gap superconductivity, room-temperature superconductivity, mesoscopic
superconductivity, the pairing state and the mechanism of cuprate high-Tc
superconductivity.
We will consider also the up-to-date state of the problem of real
construction of a quantum computer on the base of superconducting units.
InChapter1,weconsiderthefield-theoreticmethodofsuperconductivity
and discuss the basic idea of superconductivity and the elaboration of the
Ginzburg–Landau and BCS theories in the frame of many-particle quantum
field theory.
In Chapter 2, we consider such topics of high-Tc superconductivity as
the structures of high-Tc superconductors, phase diagrams, and the problem
of pseudogaps andanalyze the mechanisms of superconductivity.We present
general arguments as for the pairing symmetry in cuprate superconductors
andinvestigatetheirthermodynamicalpropertieswithinthespin-fluctuation
mechanismofsuperconductivity,byusingthemethodoffunctionalintegrals.
In Chapter 3, we consider the new class of high-temperature supercon-
ductors such as Fe-based laminar compounds.We analyze thephysical prop-
erties and electron models of Fe-based high-temperature superconductors.
Theparticularinterest inthemisexplained beperspectivesoftheir practical
application. In the chapter, we give the complete pattern of the formation
of their physical properties within theoretical models on the basis of their
electron structure.
vii
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viii Modern Aspects of Superconductivity: Theory of Superconductivity
Chapter 4 concentrates on the two-band and multiband superconductiv-
ity. Weconsiderthephysicalpropertiesof superconductorMgB anduseour
2
two-band model to explain the two coupled superconductor’s gaps of MgB .
2
TostudytheeffectoftheincreasingTc inMgB2,weusedtherenormalization
group approach and phase diagrams. In the field of superconductivity,
we meet the problem-maximum — it consists in the creation of room-
temperature superconductors. We consider this problem in our book, and
give some recommendations on the search for these superconductors.
We consider the problem of high-temperature superconductivity at high
pressures in hydrides and present the E´liashberg–Migdal theory explaining
the room-temperature superconductivity in this case.
Chapter 5 deals with the problem of nanoscale superconductivity. We
consider the two-band superconductivity in ultrasmall grains, by extending
the Richardson exact solution to two-band systems, and develop the theory
of interactions between nano-scale ferromagnetic particles and superconduc-
tors. The properties of nano-sized two-gap superconductors and the Kondo
effect in superconducting ultrasmall grains are investigated as well.
At the present time, popular is the topic of the nano-engineering with
superconducting states. In this connection, we deal with the physics of
magnetic dots on the superconductors and the problem of superconducting
wires. We analyze ideas of the quantum information and quantum calcula-
tions with the use of superconducting nano-units. We describe the theory
of the Josephson effect and its applications in quantum calculations, as well
as the idea of qubits. We consider a quantum computer on the basis of
superconducting qubits and give a short review of the modern state of the
problem of physical realization of quantum computers. We present the idea
of a topological quantum computer with qubits in the basis of Majorana
fermion quasiparticles.
This bookdeals with a widescopeof theoretical andexperimental topics
in superconductivity and is written for advanced students and researchers in
the field of superconductors.
Kyiv,
November 2020 S. Kruchinin
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Contents
Preface vii
1. Theory of Superconductivity 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Spinors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Spinor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Noether theorem and Nambu–Goldstone
theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Propagator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Non-interacting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Interacting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5.1 Unrestricted HF . . . . . . . . . . . . . . . . . . . . . . 20
1.5.2 Gap equation for superconductivity. . . . . . . . . . 21
1.6 Illustrative Example, Critical Temperature . . . . . . . . . . 22
1.6.1 Bond alternation . . . . . . . . . . . . . . . . . . . . . . 23
1.6.2 Deformation energy . . . . . . . . . . . . . . . . . . . . 24
1.6.3 Polyacene, gap equation, critical temperature . . . 25
1.6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.7 Linear Response Magnetic Resonance in Normal
and Superconducting Species: Spin-Lattice
Relaxation Time . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.7.2 T1 in NMR . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.7.3 Theory with Green’s function . . . . . . . . . . . . . 35
1.7.4 Non-interacting . . . . . . . . . . . . . . . . . . . . . . . 37
1.7.5 Interacting; normal . . . . . . . . . . . . . . . . . . . . 39
ix