Table of Contents
Foreword xiii
Tutorial on nanostructured superconductors Roger Wördenweber Johan Vanacken 1
1 Introduction 1
2 A brief history of superconductivity 1
3 Specific properties of superconductors 4
4 Theoretical understanding 4
4.1 Microscopic approach of Bardeen, Cooper, and Schrieffer 4
4.2 Thermodynamic approach of Ginzburgand Landau 7
4.3 Type-I and type-II superconductors 9
4.4 Flux pinning and summation theory 12
4.5 Flux creep and thermally assisted flux low 16
4.6 Josephson effects 17
5 Application of superconductivity 21
6 Superconductors at the nanoscale 23
1 Imaging vortices in superconductors: from the atomic scale to macroscopic distances Isabel Guillamón Jose Gabriel Rodrigo Sebastián Vieira Hermann Suderow 29
1.1 Introduction 29
1.1.1 Formalisms to treat atomic size tunneling 31
1.1.2 Electronic scattering and Fermi wavelength 32
1.1.3 Tunneling with multiple conductance channels 34
1.1.4 From tunneling into contact: Normal phase 35
1.1.5 From tunneling into contact: Superconducting phase 36
1.2 Mapping the superconducting condensate at the length scales of the coherence length and below 39
1.2.1 Gap structure and atomic size tunneling 39
1.2.2 Gap structure from Fermi sea oscillations 41
1.2.3 Gap structure and vortex shape 41
1.3 Mapping the superconducting condensate at large scales 43
1.3.1 Techniques sensing the local magnetic field 43
1.3.2 Introduction to the vortex lattice with STM 44
1.3.3 Vortex lattice melting 46
1.3.4 Vortex lattice creep 47
1.3.5 Commensurate to incommensurate transitions in nanostructured superconductors 49
1.3.6 Order-disorder transition 51
1.4 Conclusions 55
2 Probing vortex dynamics on a single vortex level by scanning ac-susceptibility microscopy Joris Van de Vondel Bart Raes Alejandro V. Silhanek 61
2.1 General introduction to ac susceptibility 61
2.1.1 AC response of a damped harmonic oscillator 62
2.1.2 AC response of a superconductor 66
2.2 Scanning susceptibility measurements 77
2.2.1 Scanning ac-susceptibility microscopy 77
2.2.2 SSM on a superconducting strip, response of individual vortices 79
2.2.3 Examples of application of the SSM technique 86
2.3 Conclusion and outlook 89
3 STM studies of vortex cores in strongly confined nanoscale superconductors Tristan Cren Christophe Brun Dimitri Roditchev 93
3.1 Introduction: Vortices in strongly confined superconductors 93
3.2 Theoretical approach of vortices confined in systems much smaller than the penetration depth 96
3.2.1 Characteristic length scales 96
3.2.2 Vortex states in small superconductors 97
3.2.3 Fluxoid 99
3.2.4 Zero-current line: Meissner versus vortex currents 100
3.2.5 Kinetic energy balance: Meissner state 101
3.2.6 Kinetic energy balance: Vortex state 101
3.2.7 Kinetic energy balance: Giant vortex state 104
3.3 STM/STS studies of vortices in nanosystems 105
3.3.1 Vortex core imaging by STM/STS 105
3.3.2 STM studies on ex situ nanolithographed samples 106
3.3.3 A model system for confinement studies: Pb/Si(111) 107
3.3.4 Ultimate confinement: The single vortex box 108
3.3.5 Confinement effect of supercurrents and surface superconductivity 113
3.3.6 Imaging of giant vortex cores 114
3.4 Proximity Josephson vortices 118
3.4.1 Proximity effect 118
3.4.2 Andreev reflection 119
3.4.3 Proximity effect in diffusive SNS junctions 119
3.4.4 Josephson vortices in S-N-S junctions 121
3.4.5 Imaging of Josephson proximity vortices 122
3.4.6 Interpretation of the vortex structure 125
3.5 Conclusion 128
4 Type-1.5 superconductivity E. Babaev J. Carlström M. Silaev J.M. Speight 133
4.1 Introduction 133
4.1.1 Type-1.5 superconductivity 135
4.2 The two-band Ginzburg-Landau model with arbitrary interband interactions. Definition of the coherence lengths and type-1.5 regime 136
4.2.1 Free energy functional 136
4.3 Coherence lengths and intervortex forces at long range in multiband superconductors 139
4.4 Critical coupling (Bogomol'nyi point) 142
4.5 Microscopic theory of type-1.5 superconductivity in U(1) multiband case 143
4.5.1 Microscopic Ginzburg-Landau expansion for U(1) two-band system 144
4.5.2 Temperature dependence of coherence lengths 146
4.6 Systems with generic breakdown of type-1/type-2 dichotomy 149
4.7 Structure of vortex clusters in the type-1.5 regime in a two-component superconductor 149
4.8 Macroscopic separation in domains of different broken symmetries in type-1.5 superconducting state 151
4.8.1 Macroscopic phase separation into U(1) × U(1) and U(1) domains in the type-1.5 regime 152
4.8.2 Macroscopic phase separation in U(1) and U(1) × Z2 domains in three-band type-1.5 superconductors 152
4.8.3 Nonlinear effects and long-range intervortex interaction in s + is superconductors 155
4.9 Fluctuation effects in type-1.5 systems 155
4.10 Misconceptions 158
4.11 Conclusion 162
5 Direct visualization of vortex patterns in superconductors with competing vortex-vortex interactions Jun-Yi Ge Vladimir N. Gladilin Joffre Gutierrez Victor V. Moshchalkov 165
5.1 Introduction 165
5.2 Classification of superconductors 166
5.2.1 Single-component superconductors 166
5.2.2 Type-1.5 superconductors 169
5.3 Experimental 170
5.4 Type-1 superconductor with long-range repulsive and short-range attractive v-v interaction 171
5.4.1 Flux patterns of the intermediate state 171
5.4.2 Topological hysteresis 174
5.4.3 Quantization of fluxoids in the intermediate state 175
5.4.4 Dynamics of flux patterns 179
5.5 Type-Il/1 superconductor with short-range repulsive and long-range attractive v-v interaction 184
5.5.1 Vortex phase diagram 184
5.5.2 Vortex pattern evolution 185
5.5.3 Vortex clusters in the IMS 188
5.6 Conclusions and outlook 189
6 Vortex dynamics in nanofabricated chemical solution deposition high-temperature superconducting films Anna Palau Victor Rouco Roberto F. Luccas Xavier Obradors Teresa Puig 195
6.1 Introduction 195
6.2 Chemical solution deposition (CSD) 196
6.2.1 Precursor solution 196
6.2.2 Solution deposition 197
6.2.3 Pyrolysis 198
6.2.4 Growth and oxygenation 198
6.3 Artificial pinning centers in CSD-YBCO films 199
6.3.1 Electron beam lithography 201
6.3.2 Focused ion beam lithography 202
6.4 Manipulating vortex dynamics in YBCO films with APC 203
6.4.1 Physical characterization techniques 203
6.4.2 Artificially ordered pinning center arrays 207
6.5 General conclusions 217
7 Artificial pinning sites and their applications Roger Wördenweber 221
7.1 Introduction 221
7.2 Artificial pinning sites 223
7.3 Vortex manipulation via antidotes 227
7.3.1 Vortex-antidot interaction and multiquanta vortices 227
7.3.2 Guided vortex motion 230
7.3.3 Vortices at high velocity 234
7.4 Artificial pinning sites in superconducting electronic devices 237
7.4.1 Flux penetration in superconducting electronic devices 237
7.4.2 Strategically positioned antidots in Josephson-junction-based devices 239
7.4.3 Antidots in microwave devices 242
7.4.4 Concepts for fluxonic devices 245
7.5 Conclusions 248
8 Vortices at microwave frequencies Enrico Silva Nicola Pompeo Oleksandr V. Dobrovolskiy 253
8.1 Introduction 253
8.2 Vortex motion complex resistivity 257
8.3 High-frequency vortex dynamics in thin films 261
8.4 Measurement techniques 262
8.5 Microwave vortex response in S/F/S heterostructures 264
8.6 Microwave vortex response in YBa2Cu3 O7-δ with nanorods 266
8.7 Microwave vortex response in Nb films with nanogroove arrays 269
8.8 Conclusion 273
8.9 Acknowledgements 273
9 Physics and operation of superconducting single-photon devices Alexander Korneev Alexander Semenov Denis Vodolazov Gregory N. Gol'tsman Roman Sobolewski 279
9.1 Introduction: what is a superconducting single-photon detector 279
9.2 Operational principles of SSPDs 282
9.2.1 Photoresponse of superconducting nanostripes 282
9.2.2 SSPDs in an external magnetic field 287
9.2.3 Origin of dark counts in SSPDs 289
9.2.4 Production of SSPD output voltage pulses 291
9.3 Methods of experimental investigation and characterization of SSPDs 294
9.3.1 SSPD fabrication 294
9.3.2 Experimental characterization of SSPDs 295
9.3.3 Demonstration of SSPD single-photon sensitivity and its detection efficiency 296
9.3.4 Measurements of SSPD timing jitter 299
9.3.5 Coupling of incoming light to SSPD as a method to increase system detection efficiency 300
9.4 Conclusion and future research directions 302
10 Josephson and charging effect in mesoscopic superconducting devices Davide Massarotti Thito Bauch Floriana Lombardi Francesco Tafuri 309
10.1 Introduction and historical background 309
10.2 Brief introductory notes on the Josephson effect: main equations, scaling energies and quantum implications 310
10.2.1 Josephson effect from quasiparticle Andreev-bound states 313
10.2.2 I-V characteristics and phase dynamics, the Resistively Shunted Junction Model 315
10.3 Why scale junctions to the 'nanoscale'? From fabrication to general properties and main parameters 321
10.3.1 Fabrication 322
10.3.2 Hybrid coplanar structures: from 2d-gas to graphene and topological insulator barriers 322
10.3.3 Submicron HTS Josephson junctions, energy scales and mesoscopic effects 325
10.4 Charging effects in ultrasmall junctions 327
10.4.1 Introduction to single-electron tunneling and parity effect 327
10.4.2 Unconventional parity effect in dx2-y2 superconductors 330
10.5 Conclusions 332
11 NanoSQUIDs: Basics & recent advances Maria José Martínez-Pérez Dieter Koelle 339
11.1 Introduction 339
11.2 SQUIDs: Some basic considerations 341
11.2.1 Resistively and capacitively shunted junction model 342
11.2.2 Dc SQUID basics 343
11.2.3 Squid readout 345
11.3 NanoSQUIDs: Design, fabrication & performance 347
11.3.1 NanoSQUIDs: Design considerations 347
11.3.2 NanoSQUIDs based on metallic superconductors 351
11.3.3 NanoSQUIDs based on cup rate superconductors 359
11.4 NanoSQUIDs for magnetic particle detection 361
11.4.1 Nanopartide positioning 361
11.4.2 Magnetization measurements 364
11.4.3 Susceptibility measurements 366
11.5 NanoSQUIDs for scanning SQUID microscopy 369
11.5.1 SQUID microscopes using devices on planar substrates 369
11.5.2 SQUID-on-tip (SOT) microscope 371
11.6 Summary and outlook 373
12 Bi2Sr2CaCu2O8 intrinsic Josephson junction stacks as emitters of terahertz radiation Reinhold Kleiner Huabing Wang 383
12.1 Introduction 383
12.2 General properties of intrinsic Josephson junctions 384
12.3 Theoretical concepts 389
12.4 Coherent THz radiation from large intrinsic Josephson junction stacks 394
13 Interference phenomena in superconductor-ferromagnet hybrids Alexander Mel'nikov Sergey Mironov Alexander Buzdin 409
13.1 Introduction 409
13.2 Josephson current through the composite ferromagnetic layer 411
13.3 Interference phenomena in nanowires 422
13.3.1 Bogoliubov-de Gennes approach 423
13.3.2 Ginzburg-Landau approach 427
13.4 Mesoscopic fluctuations 430
13.5 Conclusion 436
14 Spin-orbit interactions, spin currents, and magnetization dynamics in superconductor/ferromagnet hybrids Jacob Linder Sol H. Jacobsen 441
14.1 Spin-orbit coupling from inversion symmetry breaking: novel phenomena in SF structures 441
14.1.1 From singlet to triplet Cooper pairs 442
14.1.2 Spin-valve functionality with a single ferromagnet 444
14.1.3 Pure triplet proximity effect protected via parity symmetry 447
14.2 Controlling spin flow with superconductors 451
14.2.1 Spin supercurrents 451
14.2.2 Enhanced spin lifetimes and relaxation lengths in superconductors 454
14.3 Magnetization dynamics and spin torques in superconductors 457
14.3.1 Domain wall motion in superconducting structures 457
14.3.2 Magnetization switching and φ0-states in Josephson junctions 460
14.3.3 Spin-transfer torques tunable via the superconducting phase 463
15 Superconductor/ferromagnet hybrids Mark Giffard Blamire 473
15.1 Introduction 473
15.2 Singlet proximity coupling 475
15.3 Exchange fields and DoS splitting in superconductors 477
15.4 Triplet pairing in hybrid systems 479
15.5 Abrikosov vortex pinning in hybrid systems 480
15.6 Potential applications 481
Index 487
