Applied Superconductivity - Walther Meißner Institut - Bayerische ...

iv R. GROSS AND A. MARX CONTENTS2.2.2 The Fraunhofer Diffraction Pattern . . . . . . . . . . . . . . . . . . . . . . . . . 542.2.3 Determination of the Maximum Josephson Current Density . . . . . . . . . . . 582.2.4 Additional Topic:Direct Imaging of the Supercurrent Distribution . . . . . . . . . . . . . . . . . . 622.2.5 Additional Topic:Short Josephson Junctions: Energy Considerations . . . . . . . . . . . . . . . . 632.2.6 The Motion of Josephson Vortices . . . . . . . . . . . . . . . . . . . . . . . . . 652.3 Long Josephson Junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682.3.1 The Stationary Sine-Gordon Equation . . . . . . . . . . . . . . . . . . . . . . . 682.3.2 The Josephson Vortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702.3.3 Junction Types and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 732.3.4 Additional Topic:Josephson Current Density Distribution and Maximum Josephson Current . . . . 792.3.5 The Pendulum Analog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843 JJs: The Voltage State 893.1 The Basic Equation of the Lumped Josephson Junction . . . . . . . . . . . . . . . . . . 903.1.1 The Normal Current: Junction Resistance . . . . . . . . . . . . . . . . . . . . . 903.1.2 The Displacement Current: Junction Capacitance . . . . . . . . . . . . . . . . . 923.1.3 Characteristic Times and Frequencies . . . . . . . . . . . . . . . . . . . . . . . 933.1.4 The Fluctuation Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943.1.5 The Basic Junction Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963.2 The Resistively and Capacitively Shunted Junction Model . . . . . . . . . . . . . . . . . 973.2.1 Underdamped and Overdamped Josephson Junctions . . . . . . . . . . . . . . . 1003.3 Response to Driving Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023.3.1 Response to a dc Current Source . . . . . . . . . . . . . . . . . . . . . . . . . . 1023.3.2 Response to a dc Voltage Source . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.3.3 Response to ac Driving Sources . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.3.4 Photon-Assisted Tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1123.4 Additional Topic:Effect of Thermal Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1153.4.1 Underdamped Junctions: Reduction of I c by Premature Switching . . . . . . . . 1173.4.2 Overdamped Junctions: The Ambegaokar-Halperin Theory . . . . . . . . . . . . 1183.5 Secondary Quantum Macroscopic Effects . . . . . . . . . . . . . . . . . . . . . . . . . 1223.5.1 Quantum Consequences of the Small Junction Capacitance . . . . . . . . . . . . 122© Walther-Meißner-Institut