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Superconductivity in Nanowires: Fabrication and Quantum Transport

ISBN: 978-3-527-40832-0
282 pages
November 2012
Superconductivity in Nanowires: Fabrication and Quantum Transport (3527408320) cover image
The importance and actuality of nanotechnology is unabated and will be for years to come. A main challenge is to understand the various properties of certain nanostructures, and how to generate structures with specific properties for use in actual applications in Electrical Engineering and Medicine.

One of the most important structures are nanowires, in particular superconducting ones. They are highly promising for future electronics, transporting current without resistance and at scales of a few nanometers. To fabricate wires to certain defined standards however, is a major challenge, and so is the investigation and understanding of these properties in the first place. A promising approach is to use carbon nanotubes as well as DNA structures as templates.

Many fundamental theoretical questions are still unanswered, e.g. related to the role of quantum fluctuations. This work is tackling them and provides a detailed analysis of the transport properties of such ultrathin wires. It presents an account of theoretical models, charge transport experiments, and also conveys the latest experimental findings regarding fabrication, measurements, and theoretical analysis. In particular, it is the only available resource for the approach of using DNA and carbon nanotubes for nanowire fabrication.

It is intended for graduate students and young researchers interested in nanoscale superconductivity. The readers are assumed to have knowledge of the basics of quantum mechanics and superconductivity.
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Preface – Superconductivity and Little’s Phase Slips in Nanowires IX

Abbreviations – Short List XI

Notations – Short List XIII

Color Plates XV

1 Introduction1

2 Selected Theoretical Topics Relevant to Superconducting Nanowires 15

2.1 Free or Usable Energy of Superconducting Condensates 15

2.2 Helmholtz and Gibbs Free Energies 18

2.3 Fluctuation Probabilities 23

2.4 Work Performed by a Current Source on the Condensate in a Thin Wire 27

2.5 Helmholtz Energy of SuperconductingWires 29

2.6 Gibbs Energy of SuperconductingWires 31

2.7 Relationship between Gibbs and Helmholtz Energy Densities 35

2.8 Relationship between Thermal Fluctuations and Usable Energy 36

2.9 Calculus of Variations 38

2.10 Ginzburg–Landau Equations 39

2.11 Little–Parks Effect 46

2.12 Kinetic Inductance and the CPR of a Thin Wire 50

2.13 Drude Formula and the Density of States 51

3 Stewart–McCumberModel 53

3.1 Kinetic Inductance and the Amplitude of Small Oscillations 60

3.2 Mechanical Analogy for the Stewart–McCumber Model 62

3.2.1 Defining the Supercurrent Through Helmholtz Free Energy 65

3.2.2 Cubic Potential 66

3.2.3 Thermal Escape from the Cubic Potential 67

3.3 Macroscopic Quantum Phenomena in the Stewart–McCumber Model 68

3.3.1 MQT in a Cubic Potential at High Bias Currents 71

3.4 Schmid–Bulgadaev Quantum Phase Transition in Shunted Junctions 74

3.5 Stewart–McCumber Model with Normalized Variables 76

4 Fabrication of Nanowires Using Molecular Templates 79

4.1 Choice of Templating Molecules 86

4.2 DNA Molecules as Templates 86

4.3 Significance of the So-Called “White Spots” 88

5 Experimental Methods 91

5.1 Sample Installation 91

5.2 Electronic Transport Measurements 95

6 Resistance of Nanowires Made of Superconducting Materials 101

6.1 Basic Properties 101

6.2 Little’s Phase Slips 105

6.3 Little’s Fit 108

6.4 LAMH Model of Phase Slippage at Low Bias Currents 115

6.5 Comparing LAMH and Little’s Fit 122

7 Golubev and Zaikin Theory of Thermally Activated Phase Slips 125

8 Stochastic Premature Switching and Kurkijärvi Theory 131

8.1 Stochastic Switching Revealed by V–I Characteristics 131

8.2 “Geiger Counter” for Little’s Phase Slips 135

8.3 Measuring Switching Current Distributions 139

8.4 Kurkijärvi–Fulton–Dunkleberger (KFD) Transformation 143

8.5 Examples of Applying KFD Transformations 148

8.6 Inverse KFD Transformation 152

8.7 Universal 3/2 Power Law for Phase Slip Barrier 153

8.8 Rate of Thermally Activated Phase Slips at High Currents 157

8.9 Kurkijärvi Dispersion Power Laws of 2/3 and 1/3 160

9 Macroscopic Quantum Tunneling in Thin Wires 163

9.1 Giordano Model of Quantum Phase Slips (QPS) in Thin Wires 165

9.2 Experimental Tests of the Giordano Model 175

9.3 Golubev and Zaikin QPS Theory 183

9.4 Khlebnikov Theory 185

9.5 Spheres of Influence of QPS and TAPS Regimes 187

9.6 Kurkijärvi–Garg Model 189

9.7 Theorem: Inverse Relationship between Dispersion and the Slope of the Switching Rate Curve 195

10 Superconductor–Insulator Transition (SIT) in Thin and Short Wires 197

10.1 Simple Model of SIT in Thin Wires 207

11 Bardeen Formula for the Temperature Dependence of the Critical Current 213

Appendix A Superconductivity in MoGe Alloys 215

Appendix B Variance and the Variance Estimator 217

Appendix C Problems and Solutions 223

References 241

Index 247

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Alexey Bezryadin is Professor with the Micro- and Nanotechnology Laboratory and the Biophotonics Group at the University of Illinois at Urbana-Champaign. Previous assignments have taken him to CNRS Low-Temperature Research Center (CRTBT), France, the University of Delft, NL, and Harvard University. His research interests encompass techniques to enable novel investigations of systems with dimensions approaching 5 nm, fabrication of nanowires, loops, and SQUIDs by using carbon nanotubes as substrates, and also DNA templates.
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