Table Of ContentThe book comprises six chapters which deal with the critical
S A M I R K H E N E
currents and the ferromagnetism-superconductivity
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ii
i
Critical Currents and
Superconductivity
Ferromagnetism Coexistence in High-T Oxides
C
ii
iii
Critical Currents and
Superconductivity
Ferromagnetism Coexistence in
High-T Oxides
C
Samir Khene
Department of Physics, Faculty of Sciences
Badji Mokhtar University of Annaba
Annaba, Algeria
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2016 by Taylor & Francis Group, LLC
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Version Date: 20160419
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v
Preface
The field of superconductivity is constantly evolving. Very important
discoveries were made since the beginning of the last century; some of
them have even rewarded with Nobel Prizes.
In 1911, K.H. Onnes discovered that the electrical resistivity of many
metals vanishes below certain very low critical temperatures (Nobel Prize).
In 1933, W. Meissner and R. Ochsenfelds showed that cooled to
temperatures below its critical temperature, a superconductor expels the
magnetic field.
In 1935, F. and H. London followed in 1950 by V.L. Ginzburg and L.D.
Landau developed phenomenological theories which provided a better
understanding of superconductivity (Nobel Prize).
Based on these models, A. Abrikosov presented in 1957 a theory of the
mixed state of type-II superconductors, which stipulates that the magnetic
flux penetrates in these materials in the form of vortices (Nobel Prize).
The same year, J. Bardeen, L.N. Cooper and J.R. Schrieffers elucidated
the physical causes of the superconductivity phenomenon (Nobel Prize). In
1962, B.D. Josephson explained the tunneling junction behavior between
the superconductors (Nobel Prize). Around the same time, the discovery of
type-II superconductors which support very high magnetic fields (20 teslas)
led to their intensive use for the generation of strong fields.
In 1986, J.G. Bednorz and K.A. Muller discovered superconductivity
in a copper and lanthanum oxide doped with barium with a critical
temperature of the order of 30K (Nobel Prize). This was the beginning of
the high-T superconductors’ era.
C
The highest critical temperature reached to date is 133K in a compound
of the type HgBaCa CunO with n = 3, at ambient pressure. It reached
n-1 2n+2+d
164K in the HgBa Ca CuO compound under high pressure. With out
2 2 3 x
one well understands the physical mechanisms, responsible for the
properties of these materials. However, the common feature of these new
vi Preface
superconductors is the lamellar structure made up of elements with poor
conductivity which are juxtaposed to copper-oxygen superconducting
layers. This quasi-two-dimensional character induces in these compounds
the anisotropy of all their superconducting properties. Indeed, the
electrical conductivity is very high along the ab planes, whereas it is much
lower in the perpendicular direction to them. The critical current is very
large when the current circulates in these planes, and it is much lower in
the perpendicular direction. The critical fields are higher in the direction of
planes than in the perpendicular direction.
This book consists of six chapters. It begins by gathering key
data for superconducting state and the fundamental properties of the
conventional superconductors, followed by a recap of the basic theories
of the superconductivity. It then discusses the differences introduced
by the structural anisotropy on the Ginzburg-Landau approach and the
Lawrence-Doniach model before addressing the dynamic of vortices and
the ferromagnetism-superconductivity coexistence in high-Tc oxides,
and provides an outline of the pinning phenomena of vortices in these
materials, in particular the pinning of vortices by the spins.
This book elicits the methods to improve the properties of super-
conducting materials for industrial applications. This optimization aims
at obtaining critical temperatures and densities of critical current as high
as possible. Whereas the primary objective concerns the basic mechanisms
pushing the superconductivity towards high temperatures, the secondary
objective is to achieve a better understanding of the vortices pinning. It
is suitable for students of various streams of higher education and for
the students in the doctoral program of all branches of the fundamental
sciences and the engineering sciences. It will be beneficial to the
experienced teachers and researchers. I thank S. Senoussi, D. Feinberg,
B. Barbara and G. Fillion for all their help.
Prof. Dr. Samir Khene
Badji Mokhtar University of Annaba (Algeria)
vii
Contents
Preface v
Chapter 1: Superconducting State 1
1. History of the Superconductivity 1
2. Definition of a Superconducting Material 4
3. Meissner Effect 5
3.1. Type-I Superconductors 6
3.2. Type-II Superconductors 7
4. Description of the Superconducting State 10
4.1. Origin of Superconductivity 10
4.2. Wave Function of the Superconducting State 10
4.3. Persistent Current 11
5. Electronic Specific Heat 11
6. Electromagnetic Absorption 13
7. Isotopic Effect 14
8. Flux Quantification 14
9. Josephson Effects 15
9.1. DC Josephson Effect 16
9.2. AC Josephson Effect 17
References 17
Chapter 2: Basic Models 21
1. London Model 21
2. Phenomenological Theory of Ginzburg-Landau 27
3. BCS theory 32
3.1. Main Results of the Theory 32
3.2. Superconducting Gap 32
3.3. Comparison between Ginzburg-Landau Theory and
BCS Theory 35
References 35
viii Contents
Chapter 3: Characteristics of High-T Superconductors 37
C
1. Introduction 37
2. Crystallographic Structures 38
2.1. La M CuO (M = Ba, Sr, Ca) System 38
2-x x 4-y
2.2. RBa CuOx System 39
2 3
2.3. Thallium and Bismuth Compounds 40
2.4. Artificial Multilayers 42
3. Properties 43
4. Elaboration 43
4.1. Introduction 43
4.2. Thin Films 44
4.3. Single Crystals 46
4.4. Textured Polycrystals 47
References 48
Chapter 4: Phenomenoligical Theories of the Anisotropic
Superconductors 51
1. Anisotropic Ginzburg-Landau Model 51
1.1. Free Energy 51
1.2. Coherence Lengths 52
1.3. Penetration Depths 53
1.4. Ginzburg-Landau Parameters 54
1.5. Critical Fields 54
1.5.1. Example of the Experimental Determination of H 56
C1
1.6. Anisotropy of the Magnetization 57
1.6.1. Magnetization Near H 57
C2
1.6.2. Magnetization Within the Limit of London 58
1.6.3. Magnetization in the Interval H << H < H 58
C1 C2
1.7. Structure of the Vortices Lattice 59
1.8. Transverse Component of the Magnetization 60
2. Lawrence-Doniach Model 65
2.1. Josephson Effects 65
2.1.1. Continuous Josephson Effect 65
2.1.2. Alternative Josephson Effect 66
2.2. Free Energy 66
2.3. Characteristic Lengths 69
2.4. Change of the Dimensional Regime 70
2.4.1. Magnetic Field Parallel to the Layers 70
2.4.2. Magnetic Field Perpendicular to the Layers 73
2.4.3. Magnetic Field Inclined in Relation to the Layers 74
References 74
Chapter 5: Dynamic of Vortices 77
1. Hysteresis Origin in the Magnetization Curves 77
2. Breaking Current of Cooper Pairs 77
