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Experimental Investigations of Magnesium Diboride Josephson Junctions

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Experimental Investigations of Magnesium Diboride Josephson Junctions Experimental Investigations of Magnesium Diboride Josephson Junctions A Thesis Submitted to the Faculty of Drexel University by Steven A. Carabello in partial fulfillment of the requirements for the degree of Doctor of Philosophy May 2016 c Copyright 2016 Steven A. Carabello. This work is licensed under the terms of the Creative Commons Attribution-NonCommercial- NoDerivatives 4.0 International license. The license is available at http://creativecommons.org/licenses/by-nc-nd/4.0/. ii Acknowledgments As with any project spanning multiple years, I received help, encouragement, and support from many sources. The most direct help came from those who joined me in the ultra-low temperature laboratory at Drexel. I am especially thankful to have worked alongside Joey Lambert. We were a very effective team, and I am very grateful for his efforts. I also thank Dr. Roberto Ramos, for providing advice and support, pushes in the right direction, and for opening the world of condensed matter physics to me. Other students in the group, including Zechariah Thrailkill, Mariyan Stoyanov, Jerome Mlack, and Pubudu Galwaduge, made contributions without which I could not have achieved most of the results presented in this thesis. I am also very grateful to many others at Drexel. I thank the members of my committee for their service and support, and for keeping me on track: Dr. Bose, Dr. Barsoum, Dr. Penn, and Dr. Harb. Dr. Vogeley helped this part-time commuter student in maneuvering through all aspects of the physics graduate program. Maryann Fitzpatrick and Wolfgang Nadler were always available, encouraging, and able to help with hardware or technology of any kind. Our collaborators at Temple University and Penn State also provided fundamental support. Dr. Xiaoxing Xi inspired my investigation of magnesium diboride, and provided a great deal of support from his research group throughout my experiments. Dr. Ke Chen suggested that we explore the current-voltage characteristics for evidence of energy gap substructure, the subject of Chapter 3. And of course, no experiments could be conducted at all without experimental samples to work with. These were of extremely high quality, fabricated by Wenqing Dai and Daniel Cunnane. I thank Sigma Xi for providing a grant in aid of research, which allowed us to purchase equipment that made many of my results possible. My colleagues at Penn State Harrisburg also provided substantial support. Dr. Omid Ansary gave the initial impetus to complete my Ph.D., and supported me at every opportunity. My physics iii colleagues also made this possible, in covering classes, giving supportive words, and reviewing drafts of this thesis. So I thank Kerwin Foster, Peggy Ankney, Roger Bussard, Wolfram Bettermann, and Susan Eskin. The support of my family has been indispensable, and I am profoundly grateful. My wife, Elizabeth Carabello, has been a tremendous blessing in my life, with patience, kindness, and love beyond any reasonable expectation. My parents Nate and Gayle and my brother Chris have provided a lifetime of encouragement. My son Peter is now nearly two years old. He brings joy to every day, and everyone who knows him says, \He's such a good little boy." Finally, I thank God, for creating a world of such deep beauty. For teaching me humility. For granting me peace which surpasses all understanding. And for helping me to do more than I am able under my own strength. Soli Deo gloria. iv Table of Contents List of Tables ........................................... viii List of Figures .......................................... ix Abstract .............................................. xxii 1. Introduction .......................................... 1 1.1 Superconductivity ...................................... 2 1.1.1 Historical Background .................................. 2 1.1.2 Conduction in metals................................... 6 1.1.3 The Superconducting Energy Gap ........................... 7 1.2 Josephson Junctions ..................................... 11 1.3 Two Superconducting Energy Gaps............................. 14 1.4 Magnesium Diboride..................................... 16 2. Experiment Overview .................................... 22 2.1 Helium Dilution Refrigeration................................ 22 2.2 Noise Suppression....................................... 25 2.2.1 Environmental Isolation ................................. 27 2.2.2 High-Frequency Electronic Filtering........................... 33 2.3 Electronics .......................................... 34 2.3.1 Current Bias ....................................... 36 2.3.2 JFET Amplifier...................................... 37 2.3.3 Low-Noise Power Supply................................. 39 2.4 Junction Fabrication..................................... 42 2.4.1 Magnesium Diboride Thin Films ............................ 43 2.4.2 Josephson Junction Fabrication............................. 44 2.4.3 Junction Degradation .................................. 45 v 2.5 Mounting Samples for Measurement ............................ 46 2.6 Nb/AlOx/Nb Comparison Junctions............................ 47 2.7 Conclusion .......................................... 49 3. Current and Conductance vs. Voltage ......................... 50 3.1 Theory............................................. 50 3.1.1 Superconducting Tunnel Junctions ........................... 50 3.1.2 A Model for Multiple Energy Gaps........................... 55 3.2 Experiment Design...................................... 59 3.2.1 Electronic Apparatus................................... 59 3.2.2 Data Acquisition ..................................... 63 3.2.3 Data Analysis....................................... 64 3.2.4 System Qualification................................... 67 3.3 Results............................................. 68 3.3.1 Calculating Gap Weights................................. 68 3.3.2 Obtaining ∆P b and ∆Sn from Subgap Features.................... 71 3.3.3 π Gap Substructure ................................... 74 3.3.4 σ Gap Substructure ................................... 80 3.4 Discussion........................................... 83 3.5 Conclusion .......................................... 85 4. Superconducting-to-Normal Switching ......................... 87 4.1 Theory............................................. 88 4.1.1 The Josephson Equations ................................ 88 4.1.2 The Washboard Potential ................................ 89 4.1.3 Histograms and Escape Rates.............................. 94 4.1.4 Classical vs. Quantum Escape.............................. 96 4.1.5 Microwave Resonant Activation............................. 100 4.1.6 Escape Rate Enhancement................................ 105 TABLE OF CONTENTS TABLE OF CONTENTS vi 4.1.7 Strong Microwave Driving................................ 106 4.1.8 \Multiphoton" Transitions................................ 111 4.1.9 Effect of Hybrid Junctions................................ 114 4.2 Experiment Design...................................... 115 4.2.1 Apparatus......................................... 115 4.2.2 Keys for successful data ................................. 122 4.3 Data Analysis......................................... 123 4.3.1 Correcting Raw Switching Times............................ 123 4.3.2 Determining the Resonant Current........................... 126 4.3.3 Extracting Junction Parameters............................. 128 4.4 Results............................................. 132 4.4.1 Microwave Resonant Activation............................. 134 4.4.2 \Multiphoton" Transitions................................ 138 4.4.3 Escape Rate Enhancement................................ 145 4.4.4 Switching: Effects of Temperature ........................... 145 4.4.5 Evidence for Quantum Mechanical Behavior...................... 154 4.5 Additional Features...................................... 158 4.5.1 Microwave Resonant Activation............................. 158 4.5.2 Escape Temperature ................................... 163 4.5.3 Escape Rate Features................................... 166 4.6 Conclusions.......................................... 168 5. Conclusions and Future Work .............................. 169 5.1 Conclusions.......................................... 169 5.2 Future Work ......................................... 169 5.2.1 Magnetic Fields...................................... 169 5.2.2 Four-Wire Measurement................................. 170 5.2.3 On-Chip Isolation..................................... 172 TABLE OF CONTENTS TABLE OF CONTENTS vii 5.2.4 Additional Barrier Geometries.............................. 172 5.2.5 All-MgB2 Junctions ................................... 173 Bibliography ............................................ 174 Vita .................................................. 185 viii List of Tables 3.1 Comparison of energy gap values of MgB2 derived from fits to experimental data vs. peaks in theoretical density of states calculations. Experimental uncertainties are estimated by the range of gap values for which a 4-gap fit may produce reasonable agreement with the data. Theoretical values are based on the center of each peak (see Figure 3.18). Values for ∆σ for Theory II are approximate, as it is not easily separated into two sub-peaks. 83 4.1 Properties of the microwave coaxial cable, reproduced from [1]. Values at 293 K came from the Lake Shore Cryogenics catalog; values at 4.2K were measured by A. J. Berkley [1]. As a result of this attenuation, the
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