Superconductivity (eBook)

Richard J. Creswick, Horacio A. Farach, Charles P. Poole, Ruslan Prozorov (Autoren)

eBook Download: PDF | EPUB

2014 | 3. Auflage
870 Seiten
Elsevier Science (Verlag)
978-0-12-416610-3 (ISBN)

Infos

Superconductivity, Third Edition is an encyclopedic treatment of all aspects of the subject, from classic materials to fullerenes. Emphasis is on balanced coverage, with a comprehensive reference list and significant graphics from all areas of the published literature. Widely used theoretical approaches are explained in detail. Topics of special interest include high temperature superconductors, spectroscopy, critical states, transport properties, and tunneling. This book covers the whole field of superconductivity from both the theoretical and the experimental point of view. This third edition features extensive revisions throughout, and new chapters on second critical field and iron based superconductors. - Comprehensive coverage of the field of superconductivity - New content on magnetic properties, fluxons, anisotropies, and more - Over 2500 references to the literature - Enhanced data tables

Charles P. Poole, Jr., professor emeritus in the Department of Physics and Astronomy of the University of South Carolina, Fellow of the American Physical Society and the EPR/ESR Society, Editor of Handbook of Superconductivity and Encyclopedic Dictionary of Condensed Matter Physics. He passed away in 2015.

Inhalt

Front Cover 1
Superconductivity 4
Copyright Page 5
Dedication 6
Contents 8
Preface to the First Edition 20
Preface to the Second Edition 24
Preface to the Third Edition 28
1 Properties of the normal state 30
I Introduction 30
II Conducting electron transport 30
III Chemical potential and screening 34
IV Electrical conductivity 36
V Frequency-dependent electrical conductivity 37
VI Electron–phonon interaction 38
VII Resistivity 39
VIII Thermal conductivity 40
IX Fermi surface 41
X Energy gap and effective mass 44
XI Electronic specific heat 46
XII Phonon specific heat 47
XIII Electromagnetic fields 51
XIV Boundary conditions 52
XV Magnetic susceptibility 53
XVI Hall effect 56
Problems 59
Further Reading 60
References 60
2 Phenomenon of superconductivity 62
I Introduction 62
II Brief history 62
III Resistivity 66
A Resistivity above Tc 66
B Resistivity anisotropy 70
C Anisotropy determination 71
D Sheet resistance of films: resistance quantum 73
IV Zero resistance 76
A Resistivity drop at Tc 76
B Persistent currents below Tc 77
V Transition temperature 79
VI Perfect diamagnetism 84
VII Magnetic fields inside a superconductor 85
VIII Shielding current 88
IX Hole in superconductor 90
X Perfect conductivity 95
XI Transport current 96
XII Critical field and current 100
XIII Temperature dependences 101
XIV Two-fluid model 104
XV Critical magnetic field slope 105
XVI Critical surface 106
Problems 111
References 112
3 Transport properties 116
I Introduction 116
II Inductive superconducting circuits 116
A Parallel inductances 116
B Inductors 118
C Alternating current impedance 119
III Current density equilibration 122
IV Critical current 124
A Anisotropy 124
B Magnetic field dependence 126
V Magnetoresistance 128
A Fields applied above Tc 128
B Fields applied below Tc 130
C Fluctuation conductivity 132
D Flux flow effects 133
VI Hall effect 137
A Hall effect above Tc 137
B Hall effect below Tc 139
VII Thermal conductivity 140
A Heat and entropy transport 141
B Thermal conductivity in the normal state 142
C Thermal conductivity below Tc 145
D Magnetic field effects 147
VIII Thermoelectric and thermomagnetic effects 147
A Thermal flux of vortices 149
B Seebeck effect 150
C Nernst effect 154
D Peltier effect 157
E Ettingshausen effect 158
F Righi–Leduc effect 160
IX Photoconductivity 161
X Transport entropy 165
Problems 166
References 167
4 Thermodynamic properties 172
I Introduction 172
II Specific heat above Tc 172
III Discontinuity at Tc 179
IV Specific heat below Tc 181
V Density of states and Debye temperature 181
VI Thermodynamic variables 182
VII Thermodynamics of a normal conductor 184
VIII Thermodynamics of a superconductor 187
IX Superconductor in zero field 191
X Superconductor in a magnetic field 192
XI Normalized thermodynamic equations 199
XII Specific heat in a magnetic field 199
XIII Further discussion of the specific heat 204
XIV Order of the transition 207
XV Thermodynamic conventions 207
XVI Concluding remarks 208
Problems 209
References 210
5 Magnetic properties 212
I Introduction 212
II Susceptibility 212
III Magnetization and magnetic moment 213
IV Magnetization hysteresis 216
V ZFC and FC 217
VI Granular samples and porosity 221
VII Magnetization anisotropy 223
VIII Measurement techniques 224
IX Comparison of susceptibility and resistivity results 226
X Ellipsoids in magnetic fields 226
XI Demagnetization factors 228
XII Measured susceptibilities 229
XIII Sphere in a magnetic field 232
XIV Cylinder in a magnetic field 234
XV ac susceptibility 237
XVI Temperature-dependent magnetization 239
A Pauli-paramagnetism 240
B Paramagnetism 240
C Antiferromagnetism 242
XVII Pauli limit and upper-critical field 244
XVIII Ideal Type II superconductor 248
XIX Magnets 249
Problems 250
References 251
6 Ginzburg–Landau phenomenological theory 254
I Introduction 254
II Order parameter 254
III Ginzburg–Landau equations 255
IV Zero-field case deep inside superconductor 258
V Zero-field case near superconductor boundary 260
VI Fluxoid quantization 263
VII Penetration depth 264
VIII Critical current density 268
IX London equations 271
X Exponential penetration 272
XI Normalized Ginzburg–Landau equations 278
XII Type I and Type II superconductivity 280
XIII Upper critical field BC2 283
XIV Structure of a vortex 284
A Differential equations 284
B Solutions for short distances 285
C Solution for large distances 287
Problems 290
Further reading 291
References 292
7 Bardeen–Cooper–Schrieffer microscopic theory 294
I Introduction 294
II Cooper pairs 294
III The BCS order parameter 298
IV The BCS Hamiltonian 301
V The Bogoliubov transformation and the self-consistent gap equation 302
A Solution of the gap equation near Tc 303
B Solution at T=0 304
C Nodes of the order parameter 304
D Single band singlet pairing 304
E s-Wave pairing 305
F Zero-temperature gap 307
G d-Wave order parameter 309
H Multiband singlet pairing 311
VI Response of a superconductor to a magnetic field 314
VII Hubbard models 318
VIII Electron configurations 319
A Configurations and orbitals 319
B Tight-binding approximation 322
IX Hubbard model 326
A Wannier functions and electron operators 327
B One-state Hubbard model 328
C Electron-hole symmetry 329
D Half-filling and antiferromagnetic correlations 331
E t-J model 332
F Resonant-valence bonds 333
G Spinons, holons, slave bosons, anyons, and semions 335
H Three-state Hubbard model 335
I Energy bands 336
J Metal–insulator transition 337
X Band structure of YBa2Cu3O7 339
A Energy bands and DOS 340
B Fermi surface: plane and chain bands 343
XI Fermi liquids 343
XII Fermi surface nesting 345
XIII CDWs, SDWs, and spin bags 346
XIV Mott insulator transition 347
Problems 348
Further Reading 349
References 349
8 Type I superconductivity and the intermediate state 352
I Introduction 352
II Intermediate state 352
III Surface fields and intermediate-state configurations 353
IV Type I ellipsoid 357
V Susceptibility 359
VI Gibbs free energy for the intermediate state 360
VII Boundary-wall energy and domains 363
VIII Current-induced intermediate state 365
IX Recent developments in Type I superconductivity 371
A History and general remarks 371
B The intermediate state 375
C Magneto-optics with in-plane magnetization—a tool to study flux patterns 376
D AC response in the intermediate state of Type I superconductors 379
Problems 380
References 382
9 Type II superconductivity 384
I Introduction 384
II Internal and critical fields 384
A Magnetic field penetration 384
B Ginzburg–Landau parameter 388
C Critical fields 390
III Vortices 393
A Magnetic fields 396
B High-kappa approximation 398
C Average internal field and vortex separation 402
D Vortices near lower critical field 404
E Vortices near upper critical field 406
F Contour plots of field and current density 406
G Closed vortices 408
IV Vortex anisotropies 410
A Core region and current flow 410
B Critical fields 412
C High-kappa approximation 414
D Pancake vortices 417
E Oblique alignment 418
V Individual vortex motion 418
A Vortex repulsion 419
B Pinning 423
C Equation of motion 424
D Onset of motion 425
E Magnus force 426
F Steady-state motion 427
G Intrinsic pinning 428
H Vortex entanglement 428
VI Flux motion 429
A Flux continuum 429
B Entry and exit 430
C 2D fluid 430
D Dimensionality 431
E Solid and glass phases 432
F Flux in motion 432
G Transport current in a magnetic field 433
H Dissipation 435
I Magnetic phase diagram 435
VII Fluctuations 437
A Thermal fluctuations 437
B Characteristic length 438
C Entanglement of flux lines 438
D Irreversibility line 438
E Kosterlitz–Thouless transition 441
Problems 442
References 443
10 Irreversible magnetic properties 454
I Introduction 454
II Critical states 454
III Current–field relationships 455
A Transport and shielding current 455
B Maxwell curl equation and pinning force 456
C Determination of current–field relationships 457
IV Critical-state models 458
A Requirements of a critical-state model 458
B Model characteristics 458
V Reversed critical states and hysteresis 459
A Reversing field 460
B Magnetization 462
C Hysteresis loops 464
D Magnetization current 466
VI Perfect Type I superconductor 468
VII Concluding remarks 471
References 471
11 Magnetic penetration depth 474
I Isotropic London electrodynamics 474
II Penetration depth in anisotropic samples 476
III Experimental methods 479
IV Absolute value of the penetration depth 480
V Penetration depth and the superconducting gap 483
A Semiclassical model for superfluid density 483
a Isotropic Fermi surface 485
b Anisotropic Fermi surface, isotropic gap function 486
B Superconducting gap 486
C Mixed gaps 488
D Low temperatures 489
a s-wave pairing 489
b d-wave pairing 489
c p-wave pairing 490
VI Effect of disorder and impurities on the penetration depth 491
A Nonmagnetic impurities 491
B Magnetic impurities 493
VII Surface ABS 494
VIII Nonlocal electrodynamics of nodal superconductors 497
IX Nonlinear Meissner effect 498
X AC penetration depth in the mixed state (small amplitude linear response) 501
XI The proximity effect and its identification by using AC penetration depth measurements 504
XII Eilenberger two-gap scheme: the .-model 505
A Superfluid density 507
References 511
12 Upper critical field with magnetic and non-magnetic scattering 514
I Introduction 514
II The Bc2 Problem 515
A T& rarr
B Strong pair breaking at Tc& rarr
C Numerical results 520
III Field-dependent spin-flip scattering 521
IV The d-wave case 524
V Discussion 526
References 527
13 Energy gap and tunneling 530
I Introduction 530
II Phenomenon of tunneling 530
A Conduction-electron energies 530
B Types of tunneling 532
III Energy-level schemes 533
A Semiconductor representation 533
B Boson condensation representation 533
IV Tunneling processes 534
A Conditions for tunneling 534
B Normal metal tunneling 535
C Normal metal–superconductor tunneling 535
D Superconductor–superconductor tunneling 538
V Quantitative treatment of tunneling 540
A Distribution function 540
B Density of states 541
C Tunneling current 542
D N–I–N tunneling current 545
E N–I–S tunneling current 545
F S–I–S tunneling current 546
G Nonequilibrium quasiparticle tunneling 551
H Tunneling in unconventional superconductors 552
a Introduction 552
b Zero-bias conductance peak 553
c c-Axis tunneling 554
VI Tunneling measurements 554
A Weak links 554
B Experimental arrangements for measuring tunneling 555
C N–I–S tunneling measurements 558
D S–I–S tunneling measurements 559
E Energy gap 560
F Proximity effect 561
G Even–odd electron effect 564
VII Josephson effect 565
A Cooper-pair tunneling 565
B dc Josephson effect 566
C ac Josephson effect 569
D Driven junctions 570
E Inverse ac Josephson effect 573
F Analogues of Josephson junctions 578
VIII Magnetic field and size effects 582
A Short Josephson junction 582
B Long Josephson junction 588
C Josephson penetration depth 590
D Two-junction loop 591
E Self-induced flux 593
F Junction loop of finite size 595
G Ultrasmall Josephson junction 597
H Arrays and models for granular superconductors 598
I Superconducting quantum interference device 599
Problems 600
References 601
14 Spectroscopic properties 606
I Introduction 606
II Vibrational spectroscopy 607
A Vibrational transitions 607
B Normal modes 608
C Soft modes 610
D IR and Raman active modes 610
E Kramers–Kronig analysis 611
F IR spectra 613
G Light-beam polarization 616
H Raman spectra 618
I Energy gap 620
III Optical spectroscopy 624
IV Photoemission 629
A Measurement technique 629
B Energy levels 630
C Core-level spectra 631
D Valence band spectra 637
E Energy bands and density of states 640
V X-ray absorption edges 641
A X-ray absorption 641
B Electron-energy loss 643
VI Inelastic neutron scattering 644
VII Positron annihilation 649
VIII Magnetic resonance 653
A Nuclear magnetic resonance 653
B Quadrupole resonance 660
C Electron spin resonance 662
D Nonresonant microwave absorption 664
E Microwave energy gap 668
F Muon spin relaxation 668
G Mössbauer resonance 670
Problems 674
References 675
15 Classical superconductors 680
I Introduction 680
II Elements 680
III Physical properties of superconducting elements 683
IV Compounds 688
V Alloys 690
VI Miedema’s empirical rules 693
VII Compounds with the NaCl structure 695
VIII Type A15 compounds 697
IX Laves phases 700
X Chevrel phases 701
XI Chalcogenides and oxides 703
Problems 704
References 704
16 Cuprate high-Tc superconductors 706
I Introduction 706
II Perovskites 707
A Cubic form 707
B Tetragonal form 709
C Orthorhombic form 710
D Planar representation 712
III Perovskite-type superconducting structures 713
IV Aligned YBa2Cu3O7 716
A Copper oxide planes 718
B Copper coordination 718
C Stacking rules 719
D Crystallographic phases 720
E Charge distribution 720
F YBaCuO formula 721
G YBa2Cu4O8 and Y2Ba4Cu7O15 723
V Aligned HgBaCaCuO 724
VI Body centering 727
VII Body-centered La2CuO4, Nd2CuO4, and Sr2RuO4 729
A Unit cell of La2CuO4 compound (T phase) 730
B Layering scheme 730
C Charge distribution 731
D Superconducting structures 734
E Nd2CuO4 compound (T' phase) 735
F La2-x-y RxSryCuO4 compounds (T* phase) 736
G Sr2RuO4 compound (T phase) 737
VIII Body-centered BiSrCaCuO and TlBaCaCuO 738
A Layering scheme 738
B Nomenclature 738
C Bi–Sr compounds 739
D Tl–Ba compounds 741
E Modulated structures 742
F Aligned TI–Ba compounds 742
G Lead doping 742
IX Symmetries 743
X Layered structure of the cuprates 744
XI Infinite layer phases 747
XII Conclusion 749
Problems 750
Further reading 751
References 751
17 Noncuprate superconductors 756
I Introduction 756
II Heavy-electron systems 756
III Magnesium diboride 762
A Structure 762
B Physical properties 763
C Anisotropies 766
D Fermi surfaces 767
E Energy gaps 769
IV Borocarbides and boronitrides 770
A Crystal structure 771
B Correlations of superconducting properties with structure parameters 772
C Density of states 775
D Thermodynamic and electronic properties 777
E Magnetic interactions 780
F Magnetism of HoNi2B2C 783
V Perovskites 787
A Barium–potassium–bismuth cubic perovskite 788
B Magnesium–carbon–nickel cubic perovskite 788
C Barium–lead–bismuth lower symmetry perovskite 790
VI Charge-transfer organics 791
VII Buckminsterfullerenes 793
VIII Symmetry of the order parameter in unconventional superconductors 795
A Symmetry of the order parameter in cuprates 795
a Hole-doped high-Tc cuprates 795
b Electron-doped cuprates 796
B Organic superconductors 798
C Influence of band structure on superconductivity 801
a MgB2 802
b NbSe2 803
c CaAlSi 804
D Some other superconductors 804
a Heavy fermion superconductors 804
b Borocarbides 805
c Sr2RuO4 806
d MgCNi3 806
IX Magnetic superconductors 807
A Coexistence of superconductivity and magnetism 807
B Antiferromagnetic superconductors 809
C Magnetic cuprate superconductor (SmCeCuO) 809
References 811
18 London penetration depth in iron base superconductors 818
I Introduction 818
A Measurements of the London penetration depth 819
II TDR measurements 819
A Frequency-domain measurements 819
B Measurements of the absolute value of .(T) 821
C Out-of-plane penetration depth 821
III London penetration depth and superconducting gap 822
A London penetration depth 824
B Isotropy on a general Fermi surface 825
C 2D d-wave 825
D Eilenberger two-gap scheme: the weak-coupling model 826
E Superfluid density 827
IV Effects of scattering 831
A Gapless limit 831
V Experimental results 832
A In-plane london penetration depth 835
B Absolute value of the penetration depth 839
C Anisotropy of London penetration depths 845
D Pair-breaking 849
Conclusion 852
References 852

Textauszug

1

Properties of the normal state

The normal state is the state of a metallic material that either does not superconduct or is a superconductor at a temperature below its transition temperature Tc. This chapter emphasizes their electrical properties such as the electrical conductivity and its reciprocal the resistivity. Their temperature and frequency dependencies are given. Other properties and phenomena are explained such as the chemical potential, the electron–phonon interaction, thermal conductivity, energy gaps and effective masses, electronic and phonon specific heats, electromagnetic fields, magnetic susceptibilities, and the Hall effect. The Fermi–Dirac distribution function is emphasized. The physical properties of 14 metallic elements are tabulated.

Keywords

Electrical conduction; magnetic properties; relaxation time; Fermi–Dirac statistics; electron collisions; influence of impurities; temperature dependencies

I Introduction

This text is concerned with superconductivity, a phenomenon characterized by certain electrical, magnetic, and other properties, many of which will be introduced in the following chapter. A material becomes superconducting below a characteristic temperature, called the superconducting transition temperature Tc, which varies from very small values (millidegrees or microdegrees) to values above 100 K. The material is called normal above Tc, which merely means that it is not superconducting. Elements and compounds that become superconductors are, generally, conductors—but not good conductors—in their normal state. The good conductors, such as copper, silver, and gold, do not superconduct.

It is helpful to survey some properties of normal conductors before discussing the superconductors, so that we can review some background material and define some of the terms that will be used throughout the text. Many of the normal state properties that will be discussed here are modified in the superconducting state. Much of the material in this introductory chapter will be referred to later in the text.

II Conducting electron transport

The electrical conductivity of a metal may be described most simply in terms of the constituent atoms of the metal. In this representation, the atoms lose their valence electrons, causing a background lattice of positive ions, called cations, to form, and the now delocalized conduction electrons move between these ions. The number density n (electrons/cm3) of conduction electrons in a metallic element of density ρm (g/cm3), atomic mass number A (g/mole), and valence Z is given by

=NAZρmA, (1.1)

(1.1)

where NA is Avogadro’s number. The typical values listed in Table 1.1 are a thousand times greater than those of a gas at room temperature and atmospheric pressure.

Table 1.1

Characteristics of selected metallic elements

11 Na

1

0.97

bcc

4.23

2.65

2.08

0.8

4.2

170

32

1.38

19 K

1

1.33

bcc

5.23

1.40

2.57

1.38

6.1

180

41

1.0

29 Cu

1

0.96

fcc

3.61

8.47

1.41

0.2

1.56

210

27

4.01

47 Ag

1

1.26

fcc

4.09

5.86

1.60

0.3

1.51

200

40

4.28

41 Nb

1

1.0

bcc

3.30

5.56

1.63

3.0

15.2

21

4.2

0.52

20 Ca

2

0.99

fcc

5.58

4.61

1.73

3.43

22

2.06

38 Sr

2

1.12

fcc

6.08

3.55

1.89

7

23

14

4.4

≈0.36

56 Ba

2

1.34

bcc

5.02

3.51

1.96

17

60

6.6

1.9

≈0.19

13 Al

3

0.51

fcc

4.05

18.1

1.10

0.3

2.45

65

8.0

2.36

81 Tl

3

0.95

bcc

3.88

10.5

1.31

3.7

15

9.1

2.2

0.5

50 Sn (W)

4

0.71

Tetragonal

a=5.82

14.8

1.17

2.1

10.6

11

2.3

0.64

c=3.17

82 Pb

4

0.84

fcc

4.95

13.2

1.22

4.7

19.0

5.7

1.4

0.38

51 Sb

5

0.62

Rhombic

4.51

16.5

1.19

8

39

2.7

0.55

0.18

83 Bi

5

0.74

Rhombic

4.75

14.1

1.13

35

107

0.72

0.23

0.09

Notation: a, lattice constant; ne, conduction electron density; rs=(3/4πne)1/3; ρ, resistivity; τ, Drude relaxation time; Kth, thermal conductivity; L=ρKth/T is the Lorentz number; γ, electronic specific heat parameter; m*, effective mass; RH, Hall constant; ΘD, Debye temperature; ωp, plasma frequency in radians per femtosecond (10−15 s); IP, first ionization potential; WF, work function; EF, Fermi energy; TF, Fermi temperature in kilokelvins; kF, Fermi wavenumber in mega reciprocal centimeters; and υF, Fermi velocity in centimeters per microsecond.

The simplest approximation that we can adopt as a way of explaining conductivity is the Drude model. In this model, it is assumed that the conduction electrons

• do not interact with the cations (“free electron approximation”) except when one of them collides elastically with a cation, which happens, on average, 1/τ times per second, with the result that the velocity υ of the electron abruptly and randomly changes its direction (“relaxation time approximation”);

• maintain thermal equilibrium through collisions, in accordance with Maxwell–Boltzmann statistics (“classical statistics approximation”);

• do not interact with each other (“independent-electron approximation”).

This model predicts many of the general features of electrical conduction phenomena, as we shall see later in the chapter, but it fails to account for many others, such as tunneling, band gaps, and the Bloch T5 law. More satisfactory explanations of electron transport relax or discard one or more of these approximations.

Ordinarily, we abandon the free electron approximation by having the electrons move in a periodic potential arising from the background lattice of positive ions. Figure 1.1 shows an example of a simple potential that is negative near the positive ions and zero between them. An electron moving through the lattice interacts with the surrounding positive ions, which are oscillating about their equilibrium positions, and the charge distortions resulting from this interaction propagate along the lattice, causing distortions in the periodic potential. These distortions can influence the motion of yet another electron some distance away that is also interacting with the oscillating...

Produkt-Details

• Erscheint lt. Verlag: 22.7.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Elektrodynamik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik
• ISBN-10: 0-12-416610-5 / 0124166105
• ISBN-13: 978-0-12-416610-3 / 9780124166103