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Supervisor's Foreword; Abstract; Acknowledgements; Contents; 1 Introduction to Unconventional Superconductivity and Density Waves in Cuprates; 1.1 Superconductivity; 1.1.1 What Is a Superconductor?; 1.1.2 BCS Theory of Superconductivity; 1.2 High-Temperature Unconventional Superconductivity in Cuprates; 1.2.1 Effective Models of the CuO2 Plane; 1.2.2 Phase Diagram; 1.2.3 Anti-Ferromagnetism; 1.2.4 High-Temperature d-Wave Superconductivity; 1.2.5 Strange Metal; 1.2.6 The Pseudogap; 1.3 Charge Density Waves; 1.4 Unconventional Density Waves in Cuprates; 1.5 The Significance of CDW in Cuprates
1.6 Organisation of This ThesisReferences; 2 Spectroscopic-Imaging STM (SI-STM); 2.1 Quantum Tunnelling as a Spectroscopy; 2.1.1 Tunnelling Hamiltonian Formalism; 2.1.2 Normal-Insulator-Normal (NIN) Tunnelling; 2.1.3 Superconductor-Insulator-Normal (SIN) Tunnelling; 2.1.4 Superconductor-Insulator-Superconductor (SIS) Tunnelling; 2.2 STM
Principles; 2.3 STM
Modes of Operation; 2.3.1 Topography; 2.3.2 Spectroscopy; 2.4 SI-STM; 2.4.1 The Setup Effect; 2.4.2 Spectroscopic Functions g(""0245r,E), I(""0245r,E), Z(""0245r,E), and R(""0245r,E); 2.5 Experimental Apparatus; 2.5.1 STM Head
4 Atomic-Scale Electronic Structure of the Cuprate d-Symmetry Form Factor Charge Density Wave4.1 Form Factor Decomposition of Modulations in the CuO2 Plane; 4.2 Proposals for a d-Symmetry Form Factor CDW in Cuprates; 4.3 SI-STM Signatures of a d-Symmetry Form Factor CDW; 4.4 Detection of a d-Symmetry Form Factor CDW in Cuprates; 4.4.1 Form Factor Measurement Using Sub-Lattice Segregated SI-STM; 4.4.2 Temperature Dependence of the CDW Phenomena; 4.4.3 Short-Range Unidirectional CDW Domains; 4.5 Characteristics of CDW Modulations in the Spectral Function
4.6 Phase Relationship Between the Modulation of Filled and Empty States4.7 Doping-Dependence of the CDW Wave-Vector; 4.8 Conclusions and Proposed Future Experiments; References; 5 The Scanned Josephson Tunnelling Microscope; 5.1 Fundamentals of SJTM Operation; 5.2 The Josephson Effect as a Measure of the Superconducting Order Parameter; 5.3 Josephson Current-Voltage Characteristics in Ultra-small Junctions; 5.3.1 I(VJJ) Characteristics for Josephson Junctions with Strong Phase Coupling; 5.3.2 Thermal Phase Fluctuations in Ultra-small Josephson Junctions
1.6 Organisation of This ThesisReferences; 2 Spectroscopic-Imaging STM (SI-STM); 2.1 Quantum Tunnelling as a Spectroscopy; 2.1.1 Tunnelling Hamiltonian Formalism; 2.1.2 Normal-Insulator-Normal (NIN) Tunnelling; 2.1.3 Superconductor-Insulator-Normal (SIN) Tunnelling; 2.1.4 Superconductor-Insulator-Superconductor (SIS) Tunnelling; 2.2 STM
Principles; 2.3 STM
Modes of Operation; 2.3.1 Topography; 2.3.2 Spectroscopy; 2.4 SI-STM; 2.4.1 The Setup Effect; 2.4.2 Spectroscopic Functions g(""0245r,E), I(""0245r,E), Z(""0245r,E), and R(""0245r,E); 2.5 Experimental Apparatus; 2.5.1 STM Head
4 Atomic-Scale Electronic Structure of the Cuprate d-Symmetry Form Factor Charge Density Wave4.1 Form Factor Decomposition of Modulations in the CuO2 Plane; 4.2 Proposals for a d-Symmetry Form Factor CDW in Cuprates; 4.3 SI-STM Signatures of a d-Symmetry Form Factor CDW; 4.4 Detection of a d-Symmetry Form Factor CDW in Cuprates; 4.4.1 Form Factor Measurement Using Sub-Lattice Segregated SI-STM; 4.4.2 Temperature Dependence of the CDW Phenomena; 4.4.3 Short-Range Unidirectional CDW Domains; 4.5 Characteristics of CDW Modulations in the Spectral Function
4.6 Phase Relationship Between the Modulation of Filled and Empty States4.7 Doping-Dependence of the CDW Wave-Vector; 4.8 Conclusions and Proposed Future Experiments; References; 5 The Scanned Josephson Tunnelling Microscope; 5.1 Fundamentals of SJTM Operation; 5.2 The Josephson Effect as a Measure of the Superconducting Order Parameter; 5.3 Josephson Current-Voltage Characteristics in Ultra-small Junctions; 5.3.1 I(VJJ) Characteristics for Josephson Junctions with Strong Phase Coupling; 5.3.2 Thermal Phase Fluctuations in Ultra-small Josephson Junctions