Fundamentals and Frontiers of the Josephson Effect (Springer Series in Materials Science (286))

Description

This book provides a comprehensive and up-to-date description of the Josephson effect, a topic of never-ending interest in both fundamental and applied physics.  In this volume, world-renowned experts present the unique aspects of the physics of the Josephson effect, resulting from the use of new materials, of hybrid architectures and from the possibility of realizing nanoscale junctions. These new experimental capabilities lead to systems where novel coherent phenomena and transport processes emerge. All this is of great relevance and impact, especially when combined with the didactic approach of the book. The reader will benefit from a general and modern view of coherent phenomena in weakly-coupled superconductors on a macroscopic scale.  Topics that have been only recently discussed in specialized papers and in short reviews are described here for the first time and organized in a general framework. An important section of the book is also devoted to applications, with focus on long-term, future applications. In addition to a significant number of illustrations, the book includes numerous tables for comparative studies on technical aspects.  Preface General References Acknowledgements Contents Contributors Acronyms Symbols 1 Introductory Notes on the Josephson Effect: Main Concepts and Phenomenology 1.1 A Brief Historical Survey on the Materials Used for the Realization of Superconducting Junctions 1.2 The Coupling Between Macroscopic Quantum Systems and the Equations of the Josephson Effect 1.2.1 Josephson Equations in the Tunnel Limit 1.2.2 Different Types of Josephson Junctions Other than Tunnel 1.3 The Tunneling Hamiltonian and the Scattering Formalism 1.3.1 Expression for the Total Current in the Tunneling Hamiltonian Formalism 1.3.2 Conductance in a Tunnel Junction 1.3.3 From the Tunneling Transfer Hamiltonian to the Scattering Formalism 1.3.4 Andreev Reflection 1.3.5 Josephson Effect Derived from Quasi-particle Andreev Bound States 1.4 Current–Voltage (I–V) Characteristics: From Microscopic Theory to the Resistively Shunted Junction Model 1.4.1 I–V: Notes on the Resistively Shunted Junction Model 1.5 Temperature Dependence of Ic Rn and of the I–V characteristics 1.5.1 Temperature Dependence of Ic in the Tunnel Limit 1.5.2 Temperature Dependence of Ic Other than the Tunnel Limit 1.6 Magnetic Field Effects 1.7 Electrodynamics of the Josephson Junction 1.8 Material and Nano Science Open Novel Routes for the Fabrication of Josephson Junctions 1.8.1 Low Temperature Josephson Junctions 1.8.2 High Temperature Josephson Junctions 1.8.3 Hybrid Junctions References 2 Josephson Devices as€Tests of€Quantum Mechanics Towards the€Everyday Level 2.1 Background 2.2 Early History 2.3 Consolidation: Work on€MQT in€the€Early 80s 2.4 Progress Towards MQC: 1981–1999 2.5 The Modern Era: Josephson Qubits 2.6 Where Do We Stand? References 3 Basic Properties of the Josephson Effect 3.1 Introduction 3.2 Basic Features and Fundamental Relations 3.3 Josephson Effect in Basic Types of Junctions 3.4 SNS Junctions 3.4.1 Dirty Limit 3.4.2 Clean SNS Junctions 3.5 Double Barrier SINIS Junctions 3.5.1 SINIS Junctions, Clean Limit 3.5.2 SINIS Junctions, Dirty Limit 3.6 SFS Josephson Junctions 3.6.1 Proximity Effect in SF Bilayer 3.7 CPR in SFS Junctions 3.7.1 -Junctions 3.7.2 0-Junctions 3.7.3 CPR in Serial SIsFS and SFsFS Junctions References 4 Charge Transport in Unconventional Superconductor Junctions 4.1 Topological Superconductivity 4.1.1 Pair Potential 4.1.2 Topological Number and Surface Bound States 4.1.3 Tunnel Conductance 4.1.4 Josephson Current 4.2 Proximity Effect in a Dirty Normal Metal 4.2.1 Conductance of a Dirty NS Junction 4.2.2 Josephson Effect in a Dirty SNS Junction 4.3 Remark: Odd-Frequency Cooper Pair and Majorana Fermion References 5 Mesoscopic Features in Nanoscale Superconducting Devices 5.1 Introduction 5.2 Proximity in Macroscopic Systems 5.2.1 Free Energy of the Isolated Superconductor 5.2.2 Superconducting Correlations Induced in a Normal Metal by Proximity 5.3 Andreev Resonances at Superconductor-Normal Metal Interfaces 5.3.1 Andreev Resonances in a Clean N Slab in Proximity with a Superconductor 5.3.2 Diffusive N/S Boundary 5.3.3 Andreev Reflection Under the Magnetic Field: Magnetoconductance Oscillations in N/S Junctions 5.4 Scattering Approach to Ballistic Transport in SNS Josephson Junctions 5.4.1 Andreev Bound States with Fully Transmitting NS Interfaces 5.4.2 Density of Energy States at a Generic SNS Junction 5.5 Ballistic and Diffusive SNS Junction Systems 5.5.1 Ballistic Short and Long SNS Junctions 5.5.2 Diffusive Short and Long SNS Junctions 5.6 Semiclassical Approach to Diffusive Systems and Other Signatures of the Mesoscopic Regime 5.6.1 Minigap in SNS Diffusive Junctions 5.6.2 Low-Temperature Reentrant Behavior of the Resistance in a Diffusive N Wire in Proximity with a Superconductor 5.6.3 Resistance Change in a Wire in Contact with a Superconducting Electrode 5.7 Mesoscopic Conductance Fluctuations 5.7.1 Self Correlations of the Conductance in Magnetic Field 5.7.2 Self Correlations of the Conductance in Non Equilibrium 5.8 From Few to Single Channel Junctions 5.8.1 Shot Noise in Few Channel NS Junctions 5.8.2 Single Channel SS Junctions 5.8.3 Andreev Qubits and Parity Jumps 5.8.4 Transient Dynamics References 6 Magnetic Field Effects in Josephson Junctions 6.1 Introduction 6.2 Static Magnetic Fields 6.2.1 Flux Focussing 6.2.2 Time-Independent Sine-Gordon Equation 6.2.3 Magnetic Interference Patterns 6.2.4 Josephson Vortices 6.3 Time-Dependent Magnetic Fields 6.3.1 Time-Dependent Sine-Gordon Equation 6.3.2 Fiske Steps 6.3.3 Zero-Field Steps References 7 Current–Voltage Characteristics 7.1 The Resistively Shunted Junction Model 7.1.1 The Noise Term in the RSJ Model, a First Watch at Fluctuations 7.2 I–V Curves in the RSJ Model in the Small Capacitance Limit 7.3 I–V Curves in the RSJ Model for Finite Capacitance 7.3.1 Details of the I–V Curves in the Subgap Region for Finite Capacitance and Nonlinear RSJ Models 7.4 Current Biased Tunneling Junction, a More Accurate Description of the Subgap Region for Finite Capacitance 7.5 Effects of Thermal Fluctuations 7.5.1 Negligible Capacitance 7.5.2 Finite Capacitance 7.5.3 Large Capacitance 7.6 I–V Curves: When They Do Not Match RSJ-Like Predictions 7.6.1 Deviations from RSJ, RSJN and TJM Models 7.6.2 I–V Curves in Small or Nanoscale Junctions: From the RSJ Model to Phase Diffusion 7.6.3 Beyond Classical Smoluchowski Dynamics, from Coulomb Blockade to Quantum Diffusion 7.6.4 More on the Amplitude of the Hysteresis 7.6.5 Concluding Remarks and a Further Look at Experimental I–V Curves References 8 High Critical Temperature Superconductor Josephson Junctions and Other Exotic Structures 8.1 Introduction 8.2 Complementary Investigations and the Importance of a Structural Feedback 8.3 Grain Boundary Junctions 8.3.1 Bicrystal Junctions 8.3.2 Biepitaxial Junctions 8.3.3 Step-Edge Junctions 8.4 Locally Affecting Superconductivity, Moving Oxygen in Thin Films and Damaged Junctions 8.4.1 Modifying Junctions by Irradiation 8.4.2 Electro-Migration Studies 8.5 Junctions with an Artificial Barrier 8.5.1 Ramp Edge Junctions Realized with Au and Ag Inert Barriers 8.5.2 Ramp Edge Junctions Realized with Perosvkite and Layered Materials 8.5.3 Trilayer Structures 8.6 Interface-Engineered Junctions, a different way of Creating a Barrier 8.6.1 Ramp-Edge Junctions for Superconducting Electronics 8.7 Junctions with HTS Other Than YBCO 8.7.1 La1.85Sr0.15CuO4-Based Trilayer with One-Unit-Cell-Thick Barrier 8.7.2 Electron Doped HTS 8.8 Intrinsic Stacked Junctions 8.9 HTS Junctions and Wires on the Meso/nano Scale 8.9.1 GB Junctions Realized with Ultra-Thin Films and Superlattices 8.9.2 HTS Nanostructures and Nanowires 8.9.3 Submicron Josephson Junctions, Energy Scales and Mesoscopic Effects 8.10 General Criteria on I–V Curves and the Estimation of Junction Parameters 8.10.1 The Shape of I–V Curves 8.10.2 From I–V Curves and Their Modelling to Junction Parameters 8.10.3 Capacitance and Related Electromagnetic Properties of Junction Interfaces 8.11 Dependence of the Josephson Current on the Temperature 8.12 Notes on the Magnetic Properties of HTS Junctions 8.12.1 Dependence of the Critical Current and I–V Characteristics on the Magnetic Field 8.12.2 Spontaneous Magnetization with Random Orientation 8.13 Fractional Shapiro Steps: Time-Dependent Effects 8.14 Other Exotic Structures: Josephson Junctions Based on Interface Superconductors References 9 Pairing Symmetry Effects 9.1 Dependence of Josephson Critical Currents on Junction Geometry 9.2 Quantum Interference of Josephson Currents 9.3 Spontaneous Josephson Currents References 10 Intrinsic Josephson Junctions in High Temperature Superconductors 10.1 Introduction 10.2 Fabrication Methods and Materials 10.3 Basic Properties 10.3.1 Resistivity and Out-of-Plane Critical Current Density 10.3.2 Current Voltage Characteristics 10.3.3 Interlayer Tunneling Spectroscopy 10.3.4 Modelling of One-Dimensional Stacks: Coupling by Charge Fluctuations 10.4 Josephson Plasma Oscillations and Collective Fluxon Dynamics 10.4.1 Coupled Sine-Gordon Equations 10.4.2 Static Josephson Fluxons Lattices 10.4.3 Collective Josephson Plasma Oscillations 10.4.4 Fluxon Dynamics 10.5 Generation of THz Radiation with Intrinsic Junction Stacks References 11 Phase Dynamics and Macroscopic Quantum Tunneling 11.1 Escape Out of a Metastable State 11.1.1 Theoretical Background, Effects of Dissipation and the Underdamped Limit 11.1.2 The First Experiments 11.1.3 The Effect of the Magnetic Field on SCD 11.1.4 Notes on Resonant Activation and Quantized Energy Level 11.1.5 The Master Equation for Phase Dynamics 11.1.6 The Retrapping Current 11.1.7 Thermal Activation and Macroscopic Quantum Tunneling in SQUIDs and Annular Junctions 11.2 Moderately Damped Regime 11.3 Thermal Activation, Macroscopic Quantum Tunneling and Phase Diffusion in Unconventional Josephson Junctions 11.3.1 HTS Josephson Junctions 11.3.2 In the `Far' Low Critical Current Regime in LTS and HTS JJs 11.3.3 Phase Dynamics Diagram: Influence of Dissipation 11.3.4 Ferromagnetic Junctions 11.3.5 SCDs in Junction with Graphene Barriers 11.4 SCDs in Junctions with High Values of Jc 11.4.1 SCDs in Nanowires References 12 High Frequency Properties of Josephson Junctions 12.1 Simple Voltage Source Model 12.2 Finite Dimension Effect in Tunneling Junctions 12.3 Current Source Model 12.4 Resonant Activation References 13 Josephson Effect in Graphene and 3D Topological Insulators 13.1 Introduction 13.2 Superconductor - Graphene - Superconductor Junctions 13.3 Superconductor - Topological Insulator - Superconductor Junctions 13.4 Fabrication of Superconducting Hybrid Devices 13.5 Effective Area of a Planar Josephson Junction 13.6 Planar Josephson Junctions with TI Barriers References 14 Physics and€Applications of€NanoSQUIDs 14.1 Introduction 14.2 Superconducting “Weak-Link” Response and the Josephson Effects 14.2.1 Josephson Junctions for€NanoSQUIDs 14.2.2 Josephson Tunnel Barrier 14.2.3 Trilayer Junctions 14.2.4 Normal Metal Barriers 14.2.5 Dayem Bridge Weak Links 14.2.6 Focussed Ion Beam Milling 14.2.7 Electron Beam Lithography (EBL) 14.2.8 Niche Fabrication Developments 14.2.9 Comparison of€Tunnel Junctions and€Other Weak Links 14.3 Practical NanoSQUID Realisations 14.3.1 Grenoble Group 14.3.2 CSIRO SQUIDs 14.3.3 NPL SQUIDs 14.3.4 Other Nanosuperconducting Structures 14.3.5 Single Josephson Tunnel Junction 14.3.6 3D NanoSQUIDs 14.3.7 State-of-the-Art 14.4 Nanoscale Leads to€Improved Energy Sensitivity 14.4.1 How Reproducible is NanoSQUID Fabrication? 14.4.2 Further Miniaturization? 14.5 Applications of€NanoSQUIDs 14.5.1 Nano Electro-Mechanical Systems (NEMS) 14.6 Superconducting Qubits—At the Nanoscale? 14.7 High Frequency Readout of€SQUIDs 14.8 New Materials 14.9 Summary and€Outlook Bibliography 15 Josephson Junctions for€Metrology Applications 15.1 Introduction 15.2 Overview of€Voltage Metrology and€Applications 15.3 Voltage Quantization 15.4 Programmable DC Voltage Standards 15.5 Intrinsic AC Voltage Standards and€Arbitrary Waveform Synthesis 15.6 Temperature Metrology with€a€Quantum Voltage Noise Source References 16 Josephson Junctions for€Digital Applications 16.1 Introduction 16.2 Digital Circuits 16.2.1 Rapid Single Flux Quantum Logic 16.3 Energy-Efficient Single Flux Quantum Circuits 16.4 DC Biased Energy-Efficient Circuits 16.5 AC Biased Energy-Efficient Circuits 16.6 Adiabatic Flux Quantum Parametron Logic 16.6.1 Introduction 16.6.2 Operation Principle of€Adiabatic Quantum Flux Parametron (AQFP) Logic 16.6.3 Energy Efficiency of€an€AQFP Logic Gate 16.6.4 AQFP Logic Circuits 16.7 Memory for€Cryogenic Supercomputer 16.7.1 Introduction 16.7.2 SQUID Memory 16.7.3 Abrikosov Vortex Memory 16.7.4 Cryotron Memory 16.7.5 CMOS Memory 16.7.6 Memory Proposals Using Hybrid Superconductor/Ferromagnet Structures 16.7.7 Novel Room-Temperature Memory Proposals Considered for€Cryogenic Applications 16.7.8 Conclusion and€Outlook 16.8 Fabrication of€Low-Critical-Temperature Josephson Junctions and€Integrated Circuits 16.8.1 Introduction 16.8.2 Circuit Elements of€Superconducting Digital Circuits 16.8.3 Josephson Junctions 16.8.4 Fabrication Process 16.8.5 Nb/AlOx/Nb Josephson Junction Fabrication 16.8.6 Planarization 16.8.7 Device Structure for€Digital Circuits 16.8.8 Ic Controllability 16.8.9 Device Yield 16.8.10 Evolution of€Digital Circuit Fabrication 16.8.11 Application to€Other Superconducting Devices References 17 Quantum Bits with Josephson Junctions 17.1 Introduction 17.1.1 What Is a Qubit? 17.1.2 Why Josephson-Junction Qubits? 17.1.3 Outline 17.2 Quantizing Electrical Circuits 17.3 The Three Basic Josephson-Junction Qubits 17.3.1 Charge Qubit 17.3.2 Flux Qubit 17.3.3 Phase Qubit 17.4 Further Josephson-Junction Qubits 17.4.1 The Transmon Qubit 17.4.2 Other Qubit Refinements 17.5 Quantum Computing with Josephson-Junction Qubits 17.5.1 Fulfilling the DiVincenzo Criteria 17.5.2 Adiabatic Quantum Computing and Quantum Annealing 17.5.3 Quantum Simulation 17.5.4 Quantum Error Correction 17.6 Quantum Optics and Atomic Physics with Josephson-Junction Qubits 17.6.1 New Prospects for Textbook Quantum Optics 17.6.2 New Coupling Strengths 17.6.3 New Selection Rules 17.6.4 New Atom Sizes References 18 Quantum Superconducting Networks: From Josephson to QED Arrays 18.1 Introduction 18.2 Josephson Junction Arrays 18.2.1 Model of a Josephson Junction Array in the Quantum Regime 18.2.2 The Zero-Field Phase Diagram 18.3 Circuit-QED Arrays 18.3.1 The Model Hamiltonian of a Cavity Array 18.3.2 Effective Models 18.3.3 Open System Dynamics 18.4 Concluding Remarks: Fron Josephson to Circuit-QED Arrays References 19 Josephson Effects in Superfluid Helium 19.1 Introduction 19.2 Superfluid Weak Links 19.2.1 Josephson Equations for Quantum Fluids 19.2.2 Relevant Coupling Dimensions 19.3 Experimental Apparatus, Techniques, and Superfluid Hydrodynamics 19.3.1 Superfluid Weak Link Aperture Arrays 19.3.2 Description of Physical Cell 19.3.3 Superfluid Hydrodynamics 19.4 Josephson Dynamics in Superfluid 3He 19.4.1 Early Work 19.4.2 Superfluid 3He Josephson Oscillation 19.4.3 Superfluid 3He Plasma Mode 19.4.4 Superfluid 3He Current-Phase Relation 19.4.5 Superfluid 3He π State 19.4.6 Superfluid 3He Shapiro Effect 19.4.7 Superfluid 3He Fiske Effect 19.5 Josephson Dynamics in Superfluid 4He 19.5.1 Superfluid 4He Josephson Oscillation 19.5.2 Superfluid 4He Current-Phase Relation 19.5.3 Superfluid 4He Junction Size Effect and Phase Coherence 19.5.4 Superfluid 4He Chemical Potential ``Battery'' 19.5.5 Superfluid 4He Plasma Mode Bifurcation 19.6 Superfluid Helium Quantum Interference Devices 19.6.1 Principle of Quantum Interference in Superfluids 19.6.2 Sensitivity to ``Rotation Flux'' Instead of Magnetic Flux 19.6.3 Superfluid ``Gyrometers'' 19.6.4 Superfluid Quantum Interference Grating 19.6.5 Further Progress 19.7 Conclusion References 20 Weak Link for Ultracold Bosonic Gases 20.1 Introduction 20.2 Two Linearly Coupled Interacting Bose-Einstein Condensates 20.3 The Quantum Hamiltonian in Schwinger Collective Spin Representation 20.4 Weak Link Quantum Dynamics as Rotation and Shear of Collective Spin 20.4.1 The Most Classical Collective Spin State 20.4.2 Generalized Bloch Sphere and Husimi Representation 20.4.3 Rotation and Shear of Collective Spin 20.5 The Classical Mean Field Hamiltonian 20.6 Phase Portrait of the Classical Hamiltonian 20.7 The Analog Mechanical System—Momentum Shortened Pendulum 20.8 Experimental Realization of a Bosonic Weak Link 20.8.1 Spatial Weak Link: The Atomic Double-Well System 20.8.2 Internal Weak Link: The Atomic Two-State System 20.8.3 Overview of the Experimental Sequence 20.8.4 Control of Initial State 20.8.5 Detection of Imbalance and Relative Phase 20.9 Classical Dynamics of Macroscopic Quantum Systems 20.9.1 The First Observation of Weak Link Dynamics in Bose Einstein Condensates 20.9.2 From the Rabi to the Josephson Regime 20.9.3 The Phase Portrait of an Atomic Weak Link 20.10 Application to Thermometry—Fluctuations are the Signal References Appendix A Index